The slice is taken at a value of y, so we need to rewrite the curve y=sqrt(x-1) as x = y^2+1 The thickness of the slice and the shell is dy The radius is r = 7-y The height is h = 5-(y^2+1) = 4-y^2 The shell has volume 2pirhxx"thickness" = 2pi(7-y)(4-y^2)dy y varies from 0. Get an answer for 'y = 1 + sec(x), y = 3 Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. y 15 10 5 X х 2 4 6 8 2 4 6 8 O у 15 3 10 J 2 1 х 2 4 6 8 2 4 6 8 Sketch the solid, and a typical disk or washer. Find the volume of the solid obtained by rotating the region bounded by y=x^2,y=1; about the line y=10? Find answers now! No. Volume is 18 1/7pi To find the volume of the solid obtained by rotating the region bounded by the curves y=x^3, the x-axis and the lines x=1 and x=2 turn around the x-axis, we need to find area of the curve under the curve y=x^3, between x=1 and x=2. The volume of the solid obtained by rotating the region enclosed by y=x^3, y=16x, x≥0 about the line y=0 can be computed using the method of disks or washers via an integral The volume is V= ? cubic units. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. Include a sketch of the region and a typical cross-section with a plane orthogonal to the x-axis. using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves y=e^x, y=0, x=-2, and x=1 about the x-axis. y = 0 , y = - x 4 + 4x 3 - x 2 + 4x The region bounded by the given curves is rotated about the specified axis. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. asked by John on November 1, 2012; calculus. Find the volume of the solid obtained by rotating the region bounded by the curves y VI - 1, y = 0 and 2-5 about the 3-axis. Decide whether to integrate with respect to x or y. Solution for Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. sketch the region, the solid, and a typical disk or washer. Volume of. Advanced Math Q&A Library Find the volume of the solid obtained by rotating the region bounded by the curves x2 −y2 =9 and x=5 about the y-axis. y=2 sin(x), y=2008(*). ? | Yahoo Answers y = 3 sin(x), y = 3 cos(x), 0 ≤ x ≤ π 4 ;. 5 Sketch the sold, and a typical disk or washer. The thickness of the slice is dy, so we need the equations in the form x = a function of y. 5 OO -ast 1. Get an answer for 'Find the volume of the solid obtained by rotating the region bounded by the given curves: y=x^3, y=0, x=1, about x=2. Not entirely sure where to start?. Please see below. y = 1/x, y = 0, x = 1, x = 4; about the x-axis. $$y=\sin x, y=\cos x, 0 \leqslant x \leqslant \pi / 4 ; \quad \text { about } y=-1$$. using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves y=e^x, y=0, x=-2, and x=1 about the x-axis. $$Or you can use the disk method:$$\pi\int_{-4}^04^2-(-x)^2\,\mathrm dx+\pi\int_0^44^2-\left(\frac{x^2}4\right)^2\,\mathrm dx=\frac{1\,408}{15}\pi. 1 Questions & Answers Place. Volume is 18 1/7pi To find the volume of the solid obtained by rotating the region bounded by the curves y=x^3, the x-axis and the lines x=1 and x=2 turn around the x-axis, we need to find area of the curve under the curve y=x^3, between x=1 and x=2. Find the volume of the solid obtained by rotating the region enclosed by y=x^2, y=3x about the line x=3 using the method of disks or washers. Answer: 2π(x+2)(1−x2) dx and y = x3, x ≥ 0. Question: Find the volume of the solid obtained rotating the region between the x-axis, the y-axis, and the graph of {eq}y=\cos(x) {/eq} about (a)the z-axis;(b) the y-axis. y2 = 2x, x = 2y; about the y-axis V= Sketch the region. 0 05 05 10 1. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y=2 y=2-X 10; about the x-axis ve Sketch the region. sketch the region, the solid, and a typical disk or washer. Decide whether to integrate with respect x to y or. yox, y = x, x>0; about the x-axis ve Sketch the region. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. Find the volume of the solid obtained by rotating the region enclosed by y=x^3, y=9x, x≥0 about the line y=0 using the method of disks or washers. x=2sqrt(y), x= 0, y= 9; about the y- axis. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. Look at the first example on the last page here and try using the washer method. Image Transcriptionclose. Sketch the region enclosed by the given curves. b) Find the volume of the solid obtained by rotating the region bounded by y = 4x^2, x = 1, and y = asked by Beth on November 3, 2011; calculus. Find the volume of the solid obtained by rotating the region bounded by the graphs of the given expressions about the specified ine. y=2 sin(x), y=2008(*). The objective is to find the volume of the solid bounded by rotation about y-axis. Then find the area of the region. y = 4 − 4x^2, y = 0. y=3x, y=3x2 4. y=2x-1, y=(1/x^2); x=7. y=2/x, y = 0, x=1, x=3; about y =-1 Sketch the region then on your own sketch the solid, and a typical disk or washer. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. it would be great if you can just even give me the function inside that I. Write the integral in one variable to find the volume of the solid obtained by rotating the first-quadrant region bounded by y0. I've taken a slice perpendicular to the axis of rotation. If you could show me the steps as well, that'd be appreciated. y=1/x3,y=0,x=4,x=5;. The volume of the solid obtained by rotating the region enclosed by y=x^3, y=16x, x≥0 about the line y=0 can be computed using the method of disks or washers via an integral The volume is V= ? cubic units. sketch the region, the solid, and a typical disk or washer. Find the volume of the solid obtained by rotating the region enclosed by y=x^3, y=25x, x ≥ 0. Question: Find the volume of the solid obtained rotating the region between the x-axis, the y-axis, and the graph of {eq}y=\cos(x) {/eq} about (a)the z-axis;(b) the y-axis. y = 0, y = x (3 − x) about the axis x = 0 3. Volume = Find the volume of the solid obtained by rotating the region enclosed by the curves y = 20 - X, y = 8x + 11, x = -1 about the x-axis. How do you find the volume of the solid generated by revolving the region bounded by the graph What is the volume of the region enclosed by #y=2-0. You obtain a thin cylindrical shell of radius and height. Get an answer for 'y = 1 + sec(x), y = 3 Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. y=5x^2, x=1, y=0, about the x-axis Find the volume of the solid obtained by rotating the region bounded by the given curves. Find the volume of the solid obtained by rotating the region bounded by y = 2x − x2 the line x = −2. Find the volume of the solid obtained by rotating the region A about the line x + 2 = 0. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. find the volume obtained by rotating the region bounded by the given curves about the specified axis. y = 4 − 4x^2, y = 0. asked by John on November 1, 2012; calculus. If you want to compute this volume through the shell method, what you should compute is: $$2\pi\int_0^4y\left(2\sqrt y+y\right)\,\mathrm dy=\frac{1\,408}{15}\pi. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. -7; about y = 5 V Sketch the region. y=3x, y=3x2 4. asked • 05/13/20 Find the volume of the solid obtained by rotating the region bounded by the given curves about the line. Find the volume of the solid obtained by rotating the region bounded by the given curves. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. Solution for Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. The slice is taken at a variable value of y. If we have 2 curves y_2 and y_1 that enclose some area and we rotate that area around the x-axis, then the volume of the solid formed is given by: "Volume"=pi int_a^b[(y_2)^2-(y_1)^2]dx In the following general graph, y_2 is above y_1. y = 0 , y = - x 4 + 4x 3 - x 2 + 4x The region bounded by the given curves is rotated about the specified axis. y=2 sin(x), y=2008(*). y=3x, y=3x2 4. The answer is (3pi)/5 but I can only get (21pi)/10. Not entirely sure where to start?. Find the volume of the solid obtained by rotating the region bounded by the curves y = SQRT(x), x = 2 and y = 0 about the x-axis. Decide whether to integrate with respect x to y or.$$ Or you can use the disk method: $$\pi\int_{-4}^04^2-(-x)^2\,\mathrm dx+\pi\int_0^44^2-\left(\frac{x^2}4\right)^2\,\mathrm dx=\frac{1\,408}{15}\pi. Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis. Decide whether to integrate with respect to x or y. As the same is rotated around x-axis, we will get the volume of the desired solid. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y = 0, y = x (3 − x) about the axis x = 0 3. yox, y = x, x>0; about the x-axis ve Sketch the region. using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves y=e^x, y=0, x=-2, and x=1 about the x-axis. The objective is to find the volume of the solid bounded by rotation about y-axis. Find the volume of the solid obtained by rotating the region bounded by the curves y VI - 1, y = 0 and 2-5 about the 3-axis. I seem to be stuck on this problem. Answer: 2π(x+2)(1−x2) dx and y = x3, x ≥ 0. You obtain a thin cylindrical shell of radius and height. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Hence this volume is int_1^2pi(x^3)^2dx = int_1^2pix^6dx = pi. The objective is to find the volume of the solid bounded by rotation about y-axis. bounded by the given curves about the specifed line. 5x#, #y=0#, #x=1#, #x=2#, that is rotated See all questions in Determining the Volume of a Solid of Revolution. it would be great if you can just even give me the function inside that I. Answer to: Find the volume of the solid of revolution formed by rotating the region bounded by y = cos(x) and y = sin(2x) around the y-axis. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. Find the volume of the solid obtained by rotating the region A about the line x + 2 = 0. 5 Sketch the sold, and a typical disk or washer. 5 OO -ast 1. Here is a graph of the region. Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves x=y−y^2 and x=0 about the y-axis. Find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis. y = 1/x, y = 0, x = 1, x = 4; about the x-axis. y= x^2, y=0; x=3 about the y-axis. Here is a picture of the region with a slice taken parallel to the axis of rotation. y=sin^2 x, y=0, 0 is less then or equal to x which is less then or equal to pi; about the x-axis …. ' and find homework help for other Math questions at eNotes. Find the volume of the solid obtained by rotating the region. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Rotate such a strip (of thickness Δy) about the x-axis. asked by Thank you in advance :) on December 15, 2014; Calculus. I've taken a slice perpendicular to the axis of rotation. Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves x=y−y^2 and x=0 about the y-axis. Solution for Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Here is a graph of the region. y = 4 − 4x^2, y = 0. Please see below. Find the volume of the solid obtained by rotating the region bounded by the curves y=4x-x^2, y=8x-2x^2 about the line x=-2. у 10 6 8 4 4 2 21 х -5 LO -5 5. Find the volume of the solid obtained by rotating the region bounded by the given curves. x = 0; about the y-axis Find the volume of the solid obtained by rotating the region bounded by the given curves. If you could show me the steps as well, that'd be appreciated. y=3x, y=3x2 4. y=2 sin(x), y=2008(*). The slice is taken at a variable value of y. y=2x-1, y=(1/x^2); x=7. Here is a picture of the region with a slice taken parallel to the axis of rotation. Volume = Extra: Try to sketch the solid too! (this may be required on quizzes/exams). I've taken a slice perpendicular to the axis of rotation. Sketch the region, the solid, and a typical disk or washer.$$ y=\sin x, y=\cos x, 0 \leqslant x \leqslant \pi / 4 ; \quad \text { about } y=-1 $$. asked by Thank you in advance :) on December 15, 2014; Calculus. 0 0 Sketch the sold, and a typical disk or washer. y = 0 , y = - x 4 + 4x 3 - x 2 + 4x The region bounded by the given curves is rotated about the specified axis. Include a sketch of the region and a typical cross-section with a plane orthogonal to the x-axis. asked by Rucha on November 8, 2015; calculus. -7; about y = 5 V Sketch the region. y = 0, y = x (3 − x) about the axis x = 0 3. Find the volume of the solid obtained by rotating the region bounded by y=x^6, y=1 about the line y=4 asked Sep 15, 2011 in Calculus Answers by anonymous this is a volumes question for calculus 2. Find the volume of the solid obtained by rotating the region enclosed by the curves about the given axis. You obtain a thin cylindrical shell of radius and height. I've taken a slice perpendicular to the axis of rotation. If you want to compute this volume through the shell method, what you should compute is:$$2\pi\int_0^4y\left(2\sqrt y+y\right)\,\mathrm dy=\frac{1\,408}{15}\pi. Do not evaluate the integral. Find the volume of the solid obtained by rotating the region bounded by y = 2x − x2 the line x = −2. x = 0; about the y-axis Find the volume of the solid obtained by rotating the region bounded by the given curves. Find the volume of the solid obtained by rotating the region bounded by the curves y = SQRT(x), x = 2 and y = 0 about the x-axis. o Interactive 3D Graph O Help Interactive 3D Graph Help Interactive 30 G Help 10 1 2 -5 1 2. Get an answer for 'Find the volume of the solid obtained by rotating the region bounded by the given curves: y=x^3, y=0, x=1, about x=2. Sketch the. Find the volume of the solid obtained by rotating the region bounded by the curves. As the same is rotated around x-axis, we will get the volume of the desired solid. The slice is taken at a value of y, so we need to rewrite the curve y=sqrt(x-1) as x = y^2+1 The thickness of the slice and the shell is dy The radius is r = 7-y The height is h = 5-(y^2+1) = 4-y^2 The shell has volume 2pirhxx"thickness" = 2pi(7-y)(4-y^2)dy y varies from 0. 5 Sketch the sold, and a typical disk or washer. Find the volume of the solid obtained by rotating the region bounded by the given curves about the line x= -6 y= x^2 x= y^2. bounded by the given curves about the specifed line. Sketch the region, the solid, and a. Question Asked Aug 30, 2020. $$y=\sin x, y=\cos x, 0 \leqslant x \leqslant \pi / 4 ; \quad \text { about } y=-1$$. 1 Questions & Answers Place. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Dominique S. x=2sqrt(y), x= 0, y= 9; about the y- axis. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. Find the volume of the solid obtained by rotating the region enclosed by y=x^2, y=3x about the line x=3 using the method of disks or washers. [College Calculus 1] Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. To find the volume of the solid of revolution obtained by revolving the region bounded by : The equations {eq}y = x^2 {/eq}, the tangent line to this equation at {eq}x = -1\Rightarrow y=-2x-1 {/eq},. Hence this volume is int_1^2pi(x^3)^2dx = int_1^2pix^6dx = pi. y=1/x3,y=0,x=4,x=5;. it would be great if you can just even give me the function inside that I. Volume = Find the volume of the solid obtained by rotating the region enclosed by the curves y = 20 - X, y = 8x + 11, x = -1 about the x-axis. Then find the area of the region. Sketch the region, the solid, and a typical disk or washer. Rotate such a strip (of thickness Δy) about the x-axis. Look at the first example on the last page here and try using the washer method. asked • 08/23/15 find the volume of the solid obtained by rotating the region bounded by xy=4 and y=(x-3)^2 about the x-axis. Use washer method to find the volume of the solid. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line: (a) y = 1 + sec(x), y = 3; about y = 1. Find the volume V of the solid obtained by rotating the region bounded by the graphs of the given expressions about the specified line. Sketch the region, the solid, and a. y=2 sin(x), y=2008(*). When a two-dimensional region is revolved about an axis lying in the same plane, a solid volume is obtained. y = 4 − 4x^2, y = 0. Solution for Find the volume of the solid obtained by rotating the region bounded by the curves x2 −y2 =9 and x=5 about the y-axis. Find the volume of the solid obtained by rotating the region bounded by the graphs of the given expressions about the specified line. Answer to: Find the volume of the solid obtained by rotating the region bounded by the curves y^{2}=x and x=2y about the y-axis. y 15 10 5 X х 2 4 6 8 2 4 6 8 O у 15 3 10 J 2 1 х 2 4 6 8 2 4 6 8 Sketch the solid, and a typical disk or washer. Hence this volume is int_1^2pi(x^3)^2dx = int_1^2pix^6dx = pi. Rotate such a strip (of thickness Δy) about the x-axis. ' and find homework help for other Math questions at eNotes. Then find the area of the region. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. 5 OO -ast 1. If we have 2 curves y_2 and y_1 that enclose some area and we rotate that area around the x-axis, then the volume of the solid formed is given by: "Volume"=pi int_a^b[(y_2)^2-(y_1)^2]dx In the following general graph, y_2 is above y_1. Question: Find the volume of the solid obtained rotating the region between the x-axis, the y-axis, and the graph of {eq}y=\cos(x) {/eq} about (a)the z-axis;(b) the y-axis. Question Asked Aug 30, 2020. y = x + 1, y = 0, x = 0, x = 4; about the x-axis. Find the volume of the solid obtained by rotating the region bounded by y = 2x − x2 the line x = −2. y = 4 − 4x^2, y = 0. y=2 sin(x), y=2008(*). Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. $$Or you can use the disk method:$$\pi\int_{-4}^04^2-(-x)^2\,\mathrm dx+\pi\int_0^44^2-\left(\frac{x^2}4\right)^2\,\mathrm dx=\frac{1\,408}{15}\pi. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. You obtain a thin cylindrical shell of radius and height. A Solid of Revolution. Please see below. 0 05 05 10 1. asked by Rucha on November 8, 2015; calculus. y=2 sin(x), y=2008(*). Decide whether to integrate with respect x to y or. asked by Becca on September 25, 2011. Get an answer for 'Find the volume of the solid obtained by rotating the region bounded by the given curves: y=x^3, y=0, x=1, about x=2. asked • 05/31/16 Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 0, y = x (3 − x) about the axis x = 0 3. Decide whether to integrate with respect to x or y. [College Calculus 1] Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. o Interactive 3D Graph O Help Interactive 3D Graph Help Interactive 30 G Help 10 1 2 -5 1 2. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. 5 OO -ast 1. As the same is rotated around x-axis, we will get the volume of the desired solid. Find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis. y= x^2, y=0; x=3 about the y-axis. Solution for Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. x = 0; about the y-axis Find the volume of the solid obtained by rotating the region bounded by the given curves. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. You obtain a thin cylindrical shell of radius and height. find the volume obtained by rotating the region bounded by the given curves about the specified axis. Hence this volume is int_1^2pi(x^3)^2dx = int_1^2pix^6dx = pi. Let A be the bounded region enclosed by the graphs of f(x) = x , g(x) = x3. Find the volume of the solid obtained by rotating the region bounded by y=x^2,y=1; about the line y=10? Find answers now! No. Find the volume of the solid obtained by rotating the region bounded by the graphs of the given expressions about the speed line y=5+ secta) sus. y=2/x, y = 0, x=1, x=3; about y =-1 Sketch the region then on your own sketch the solid, and a typical disk or washer. 1 Questions & Answers Place. -7; about y = 5 V Sketch the region. I seem to be stuck on this problem. Find the volume of the solid obtained by rotating the region enclosed by y=x^3, y=9x, x≥0 about the line y=0 using the method of disks or washers. Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 4 − 4x^2, y = 0. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. The slice is taken at a variable value of y. Sketch the. The curve on the left (y = sqrtx) is x = y^2 on the right is the line x = y Rotating the slice will generate a washer of thickness dy and volume pi(R^2. y = x + 1, y = 0, x = 0, x = 4; about the x-axis. Find the volume V of the solid obtained by rotating the region bounded by the graphs of the given expressions about the specified line. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. Find the volume of the solid obtained by rotating the region enclosed by the lines… 2 Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. x=2sqrt(y), x= 0, y= 9; about the y- axis. Find the volume of the solid obtained by rotating the region bounded by the graphs of the given expressions about the specified line. Then use this information to estimate the volume of the solid obtained by rotating about the y-axis the region enclosed by these curves. Decide whether to integrate with respect to x or y. asked by me on October 31, 2010. Include a sketch of the region and a typical cross-section with a plane orthogonal to the x-axis. Find the volume of the solid obtained by rotating the region bounded by the graphs of the given expressions about the specified ine. Sketch the. By signing up,. asked • 05/31/16 Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. Find the volume of the solid obtained by rotating the region bounded by y = 2x − x2 the line x = −2. asked • 08/23/15 find the volume of the solid obtained by rotating the region bounded by xy=4 and y=(x-3)^2 about the x-axis. 5x2 and yx about the line x7. Let A be the bounded region enclosed by the graphs of f(x) = x , g(x) = x3. Image Transcriptionclose. y = 9 - 9x^2 , y = 0 Find the volume V of this solid. The slice is taken at a variable value of y. Volume = Find the volume of the solid obtained by rotating the region enclosed by the curves y = 20 - X, y = 8x + 11, x = -1 about the x-axis. The volume sol obtained is symmetric about the axis of rotation. y=2 y=2-X 10; about the x-axis ve Sketch the region. I've taken a slice perpendicular to the axis of rotation. y2 = 2x, x = 2y; about the y-axis V= Sketch the region. Solution for Find the volume of the solid obtained by rotating the region bounded by the curves x2 −y2 =9 and x=5 about the y-axis. Solution for Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Area of cross-section in the plane has the shape of a washer (an annular ring) with inner radius and outer radius is as follows:. y=sin^2 x, y=0, 0 is less then or equal to x which is less then or equal to pi; about the x-axis …. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. region, the solid, and a typical disk or washer. Volume is 18 1/7pi To find the volume of the solid obtained by rotating the region bounded by the curves y=x^3, the x-axis and the lines x=1 and x=2 turn around the x-axis, we need to find area of the curve under the curve y=x^3, between x=1 and x=2. I seem to be stuck on this problem. Find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis. The volume of the solid obtained by rotating the region enclosed by y=x^3, y=16x, x≥0 about the line y=0 can be computed using the method of disks or washers via an integral The volume is V= ? cubic units. Decide whether to integrate with respect x to y or. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. у 10 6 8 4 4 2 21 х -5 LO -5 5. If we have 2 curves y_2 and y_1 that enclose some area and we rotate that area around the x-axis, then the volume of the solid formed is given by: "Volume"=pi int_a^b[(y_2)^2-(y_1)^2]dx In the following general graph, y_2 is above y_1. By signing up,. Find the volume of the solid obtained by rotating the region bounded by y=x^6, y=1 about the line y=4 asked Sep 15, 2011 in Calculus Answers by anonymous this is a volumes question for calculus 2. у 10 6 8 4 4 2 21 х -5 LO -5 5. y = 0 , y = - x 4 + 4x 3 - x 2 + 4x The region bounded by the given curves is rotated about the specified axis. Question Asked Aug 30, 2020. Answer to: Find the volume of the solid obtained by rotating the region enclosed by the curves y = x^2, y = 12x, and x = 0 for x greater than 0. 5 OO -ast 1. Not entirely sure where to start?. (b) y = x 2 and y = −x 2 + 4 about the x−axis. Question: Find the volume of the solid obtained rotating the region between the x-axis, the y-axis, and the graph of {eq}y=\cos(x) {/eq} about (a)the z-axis;(b) the y-axis. If you could show me the steps as well, that'd be appreciated. asked • 05/13/20 Find the volume of the solid obtained by rotating the region bounded by the given curves about the line. How do you find the volume of the solid generated by revolving the region bounded by the graph What is the volume of the region enclosed by #y=2-0. y= x^2, y=0; x=3 about the y-axis. y = 4 − 4x^2, y = 0. y=1/x^2 y=0 x=4 x=7; about y=–3 i integrated and plugged in values for x and got. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. When a two-dimensional region is revolved about an axis lying in the same plane, a solid volume is obtained. Volume = Find the volume of the solid obtained by rotating the region enclosed by the curves y = 20 - X, y = 8x + 11, x = -1 about the x-axis. asked • 08/23/15 find the volume of the solid obtained by rotating the region bounded by xy=4 and y=(x-3)^2 about the x-axis. A Solid of Revolution. Volume = Find The Volume Of The Solid Obtained By Rotating The Region Enclosed By The Curves Y = 20 - X, Y = 8x + 11, X = -1 About The X-axis. 5 Sketch the sold, and a typical disk or washer. The answer is (3pi)/5 but I can only get (21pi)/10. Find the volume V of the solid obtained by rotating the region bounded by the graphs of the given expressions about the specified line. y = 4 − 4x^2, y = 0. Volume = Find the volume of the solid obtained by rotating the region enclosed by the curves y = 20 - X, y = 8x + 11, x = -1 about the x-axis. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. y 15 10 5 X х 2 4 6 8 2 4 6 8 O у 15 3 10 J 2 1 х 2 4 6 8 2 4 6 8 Sketch the solid, and a typical disk or washer. The volume of the solid obtained by rotating the region enclosed by y=x^3, y=16x, x≥0 about the line y=0 can be computed using the method of disks or washers via an integral The volume is V= ? cubic units. As the same is rotated around x-axis, we will get the volume of the desired solid. Then find the area of the region. o Interactive 3D Graph O Help Interactive 3D Graph Help Interactive 30 G Help 10 1 2 -5 1 2. Rotate such a strip (of thickness Δy) about the x-axis. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. 61 *pi this is not the right answer been trying for hours please help!. Find the volume of the solid obtained by rotating the region bounded by the graphs of the given expressions about the specified line. Find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis. Find the volume of the solid obtained by rotating the region bounded by y=x^2,y=1; about the line y=10? Find answers now! No. By signing up,. The curve on the left (y = sqrtx) is x = y^2 on the right is the line x = y Rotating the slice will generate a washer of thickness dy and volume pi(R^2. 0 0 Sketch the sold, and a typical disk or washer. Answer to: Find the volume of the solid of revolution formed by rotating the region bounded by y = cos(x) and y = sin(2x) around the y-axis. Find the points of intersection of the curves: The curves intersect at the points and. y = 1/x, y = 0, x = 1, x = 4; about the x-axis. Find the volume of the solid obtained by rotating the region bounded by the curves y = SQRT(x), x = 2 and y = 0 about the x-axis. Find the volume of the solid obtained by rotating the region bounded by the curves y VI - 1, y = 0 and 2-5 about the 3-axis. No, it is not correct. Find the volume of the solid obtained by rotating the region enclosed by the curves about the given axis. Volume is 18 1/7pi To find the volume of the solid obtained by rotating the region bounded by the curves y=x^3, the x-axis and the lines x=1 and x=2 turn around the x-axis, we need to find area of the curve under the curve y=x^3, between x=1 and x=2. bounded by the given curves about the specifed line. -5 5 -5 5. Answer: 2π(x+2)(1−x2) dx and y = x3, x ≥ 0. Here is a graph of the region. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=2 sin(x), y=2008(*). y=5x^2, x=1, y=0, about the x-axis Find the volume of the solid obtained by rotating the region bounded by the given curves. Find the volume of the solid obtained by rotating the region enclosed by the curves y = x? y = 6 - x, X=0 for x > 0 about the line y = 7. y у 10 8H 6 2. Sketch the region and a typical disk or washer. 5x#, #y=0#, #x=1#, #x=2#, that is rotated See all questions in Determining the Volume of a Solid of Revolution. Volume is 18 1/7pi To find the volume of the solid obtained by rotating the region bounded by the curves y=x^3, the x-axis and the lines x=1 and x=2 turn around the x-axis, we need to find area of the curve under the curve y=x^3, between x=1 and x=2. Find the volume of the solid obtained by rotating the region enclosed by y=x^3, y=9x, x≥0 about the line y=0 using the method of disks or washers. asked • 05/13/20 Find the volume of the solid obtained by rotating the region bounded by the given curves about the line. Sketch the region, the solid, and a typical disk orwasher. How do you find the volume of the solid generated by revolving the region bounded by the graph What is the volume of the region enclosed by #y=2-0. The thickness of the slice is dy, so we need the equations in the form x = a function of y. I would use shells. The volume of the solid obtained by rotating the region enclosed by y=1/x4,y=0,x=1,x=6 about the line x=−2 can be computed using the method of cylindrical shells via an integral. Not entirely sure where to start?. Please see below. yox, y = x, x>0; about the x-axis ve Sketch the region. Find the volume of the solid obtained by rotating the region bounded by y=x^6, y=1 about the line y=4 asked Sep 15, 2011 in Calculus Answers by anonymous this is a volumes question for calculus 2. Answer: 2π(x+2)(1−x2) dx and y = x3, x ≥ 0. y = ln x, y = 1, y = 2. y = x + 1, y = 0, x = 0, x = 4; about the x-axis. I've taken a slice perpendicular to the axis of rotation. Find the volume of the solid obtained by rotating the region enclosed by the curves y = x? y = 6 - x, X=0 for x > 0 about the line y = 7. Answer to: Find the volume of the solid of revolution formed by rotating the region bounded by y = cos(x) and y = sin(2x) around the y-axis. 0 05 05 10 1. Then use your calculator to evaluate the integral correct to five decimal places. o Interactive 3D Graph O Help Interactive 3D Graph Help Interactive 30 G Help 10 1 2 -5 1 2. If you want to compute this volume through the shell method, what you should compute is: $$2\pi\int_0^4y\left(2\sqrt y+y\right)\,\mathrm dy=\frac{1\,408}{15}\pi. y=1/x3,y=0,x=4,x=5;. Find the volume of the solid obtained by rotating the region bounded by y=x^6, y=1 about the line y=4 asked Sep 15, 2011 in Calculus Answers by anonymous this is a volumes question for calculus 2. Consider the solid obtained by rotating the region bounded by the given curves about the x-axis. Advanced Math Q&A Library Find the volume of the solid obtained by rotating the region bounded by the curves x2 −y2 =9 and x=5 about the y-axis. Then find the area of the region. Answer: 2π(x+2)(1−x2) dx and y = x3, x ≥ 0. Question Asked Aug 30, 2020. Include a sketch of the region and a typical cross-section with a plane orthogonal to the x-axis. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line: (a) y = 1 + sec (x), y = 3; about y = 1. Find the volume of the solid obtained by rotating the region bounded by y? = x + 4 and 6 - x about the line y = -6 by using: 3 a) The method of Cylindrical Shells. Find the volume of the solid obtained by rotating the region enclosed by y=x^3, y=9x, x≥0 about the line y=0 using the method of disks or washers. Find the volume of the solid obtained by rotating the region under the graph of f(x)= 9-x^2 for 0. (b) y = x 2 and y = −x 2 + 4 about the x−axis. y=2/x, y = 0, x=1, x=3; about y =-1 Sketch the region then on your own sketch the solid, and a typical disk or washer. Decide whether to integrate with respect to x or y. it would be great if you can just even give me the function inside that I. y = 4 − 4x^2, y = 0. Find the volume of the solid obtained by rotating the region bounded by the curves y = SQRT(x), x = 2 and y = 0 about the x-axis. Find the volume of the solid obtained by rotating the region enclosed by y=x^3, y=9x, x≥0 about the line y=0 using the method of disks or washers. Consider the solid obtained by rotating the region bounded by the given curves about the x-axis. Find the volume of the solid obtained by rotating the region enclosed by y=x^2, y=3x about the line x=3 using the method of disks or washers. asked by me on October 31, 2010. y = x + 1, y = 0, x = 0, x = 2; about the x-axis V = Sketch the region. Find the volume of the solid obtained by rotating the region bounded by the given curves. Answer to: Find the volume of the solid obtained by rotating the region enclosed by the curves y = x^2, y = 12x, and x = 0 for x greater than 0. Find the points of intersection of the curves: The curves intersect at the points and. y= x^2, y=0; x=3 about the y-axis. Find the volume of the solid obtained by rotating the region bounded by the curves y=4x-x^2, y=8x-2x^2 about the line x=-2. 5x2 and yx about the line x7. Find the volume of the solid obtained by rotating the region. Answer to: Find the volume of the solid of revolution formed by rotating the region bounded by y = cos(x) and y = sin(2x) around the y-axis. asked by Rucha on November 8, 2015; calculus. 0 0 Sketch the sold, and a typical disk or washer. y = 4 − 4x^2, y = 0. Find the volume of the solid obtained by rotating the region enclosed by the lines… 2 Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. Question Asked Aug 30, 2020. Not entirely sure where to start?. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. Find the volume of the solid obtained by rotating the region enclosed by the lines… 2 Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. Get an answer for 'y = 1 + sec(x), y = 3 Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 0 , y = - x 4 + 4x 3 - x 2 + 4x The region bounded by the given curves is rotated about the specified axis. Get an answer for 'Find the volume of the solid obtained by rotating about y axis the region between y=x and y=x^2. find the volume obtained by rotating the region bounded by the given curves about the specified axis. How do you find the volume of the solid generated by revolving the region bounded by the graphs #y=1/x, y=0, x=1, x=4#, about the x axis? Calculus Applications of Definite Integrals Determining the Volume of a Solid of Revolution. y2 = 2x, x = 2y; about the y-axis V= Sketch the region. region, the solid, and a typical disk or washer. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Please see below. Find the volume of the solid obtained by rotating the region bounded by the curves y VI - 1, y = 0 and 2-5 about the 3-axis. у 10 6 8 4 4 2 21 х -5 LO -5 5. Find the volume of the solid obtained by rotating the region. y=2 sin(x), y=2008(*). y = 0, y = x (3 − x) about the axis x = 0 3. A Solid of Revolution. Please round the answers to the nearest hundredth. y=1/x3,y=0,x=4,x=5;. Then find the area of the region. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. Find the volume of the solid obtained by rotating the region bounded by the graphs of the given expressions about the specified line. x=2sqrt(y), x= 0, y= 9; about the y- axis. Find the volume V of the solid obtained by rotating the region bounded by the graphs of the given expressions about the specified line. I've taken a slice perpendicular to the axis of rotation. Please see below. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis. Sketch the. find the volume obtained by rotating the region bounded by the given curves about the specified axis. Answer to: Find the volume of the solid of revolution formed by rotating the region bounded by y = cos(x) and y = sin(2x) around the y-axis. Look at the first example on the last page here and try using the washer method. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. sketch the region, the solid, and a typical disk or washer. I would use shells. asked by John on November 1, 2012; calculus. y=2 y=2-X 10; about the x-axis ve Sketch the region. xy = 2, x = 0, y = 2, y = 4 Answer Save. 5x#, #y=0#, #x=1#, #x=2#, that is rotated See all questions in Determining the Volume of a Solid of Revolution. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y = 0 , y = - x 4 + 4x 3 - x 2 + 4x The region bounded by the given curves is rotated about the specified axis. In questions 2, 3 and 5, give the answers in exact form (not a decimal approximation). r = y (distance from strip to axis of rotation) h = x = 12√ (y) (length of strip. Decide whether to integrate with respect to x or y. Find the volume of the solid obtained by rotating the region A about the line x + 2 = 0. 5 OO -ast 1. The volume of the solid obtained by rotating the region enclosed by y=1/x4,y=0,x=1,x=6 about the line x=−2 can be computed using the method of cylindrical shells via an integral. y= x^2, y=0; x=3 about the y-axis. asked by Thank you in advance :) on December 15, 2014; Calculus. Get an answer for 'y = 1 + sec(x), y = 3 Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. I've taken a slice perpendicular to the axis of rotation. y=5x^2, x=1, y=0, about the x-axis Find the volume of the solid obtained by rotating the region bounded by the given curves. y = 4 − 4x^2, y = 0. ' and find homework help for other Math questions at eNotes. 5x2 and yx about the line x7. yox, y = x, x>0; about the x-axis ve Sketch the region. The slice is taken at a variable value of y. Get an answer for 'y = 1 + sec(x), y = 3 Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. The objective is to find the volume of the solid bounded by rotation about y-axis. 5x2 and yx about the line x7. Rotate such a strip (of thickness Δy) about the x-axis. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. Question Asked Aug 30, 2020. Decide whether to integrate with respect x to y or. Sketch the region, the solid, and a. Find the volume of the solid obtained by rotating the region bounded by y = 2x − x2 the line x = −2. Sketch the region, the solid, and a typical disk or washer. Find the volume of the solid obtained by rotating the region bounded by the curves y VI - 1, y = 0 and 2-5 about the 3-axis. Volume by Rotating the Area Enclosed Between 2 Curves. Hence this volume is int_1^2pi(x^3)^2dx = int_1^2pix^6dx = pi. Find the volume of the solid obtained by rotating the region. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Then use this information to estimate the volume of the solid obtained by rotating about the y-axis the region enclosed by these curves. The curve on the left (y = sqrtx) is x = y^2 on the right is the line x = y Rotating the slice will generate a washer of thickness dy and volume pi(R^2. y = x + 1, y = 0, x = 0, x = 2; about the x-axis V = Sketch the region. y = ln x, y = 1, y = 2. 0 0 Sketch the sold, and a typical disk or washer. The slice is taken at a variable value of y. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.$$ y=\sin x, y=\cos x, 0 \leqslant x \leqslant \pi / 4 ; \quad \text { about } y=-1 $$. Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves x=y−y^2 and x=0 about the y-axis. -7; about y = 5 V Sketch the region. In questions 2, 3 and 5, give the answers in exact form (not a decimal approximation). Find the volume of the solid obtained by rotating the region under the graph of f(x)= 9-x^2 for 0. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. asked by John on November 1, 2012; calculus. y = 0, y = x (3 − x) about the axis x = 0 3. y = 1/x, y = 0, x = 1, x = 4; about the x-axis. Volume by Rotating the Area Enclosed Between 2 Curves. y=1/x3,y=0,x=4,x=5;. A Solid of Revolution. Find the volume of the solid obtained by rotating the region under the graph f(x) = x2 - 3x about the x-axis over the interval [0, 3]. Find the volume of the solid obtained by rotating the region bounded by the curves. Then use your calculator to evaluate the integral correct to five decimal places. The objective is to find the volume of the solid bounded by rotation about y-axis. y=3x, y=3x2 4. y = x + 1, y = 0, x = 0, x = 2; about the x-axis V = Sketch the region. Volume is 18 1/7pi To find the volume of the solid obtained by rotating the region bounded by the curves y=x^3, the x-axis and the lines x=1 and x=2 turn around the x-axis, we need to find area of the curve under the curve y=x^3, between x=1 and x=2. y = 0 , y = - x 4 + 4x 3 - x 2 + 4x The region bounded by the given curves is rotated about the specified axis. 0 05 05 10 1. Find the volume of the solid obtained by rotating the region bounded by the graphs of the given expressions about the specified line. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. If we have 2 curves y_2 and y_1 that enclose some area and we rotate that area around the x-axis, then the volume of the solid formed is given by: "Volume"=pi int_a^b[(y_2)^2-(y_1)^2]dx In the following general graph, y_2 is above y_1. у 10 6 8 4 4 2 21 х -5 LO -5 5. 0 0 Sketch the sold, and a typical disk or washer. 5 Sketch the sold, and a typical disk or washer. Please round the answers to the nearest hundredth. y= x^2, y=0; x=3 about the y-axis. The answer is (3pi)/5 but I can only get (21pi)/10. (b) y = x 2 and y = −x 2 + 4 about the x−axis. asked • 08/23/15 find the volume of the solid obtained by rotating the region bounded by xy=4 and y=(x-3)^2 about the x-axis. Get an answer for 'y = 1 + sec(x), y = 3 Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region and a typical disk or washer. y=5x^2, x=1, y=0, about the x-axis Find the volume of the solid obtained by rotating the region bounded by the given curves. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. The thickness of the slice is dy, so we need the equations in the form x = a function of y. Find the volume of the solid obtained by rotating the region bounded by the graphs of the given expressions about the speed line y=5+ secta) sus. Decide whether to integrate with respect to x or y. Question: Find the volume of the solid obtained rotating the region between the x-axis, the y-axis, and the graph of {eq}y=\cos(x) {/eq} about (a)the z-axis;(b) the y-axis. y = x + 1, y = 0, x = 0, x = 2; about the x-axis V = Sketch the region. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Write the integral in one variable to find the volume of the solid obtained by rotating the first-quadrant region bounded by y0. If we have 2 curves y_2 and y_1 that enclose some area and we rotate that area around the x-axis, then the volume of the solid formed is given by: "Volume"=pi int_a^b[(y_2)^2-(y_1)^2]dx In the following general graph, y_2 is above y_1. y=sin^2 x, y=0, 0 is less then or equal to x which is less then or equal to pi; about the x-axis …. Find the volume of the solid obtained by rotating the region bounded by the curves x2 −y2 =9 and x=5 about the y-axis. Sketch the region, the solid, and a typical disk or washer. Sketch the region, the solid, and a. y=2/x, y = 0, x=1, x=3; about y =-1 Sketch the region then on your own sketch the solid, and a typical disk or washer. If you could show me the steps as well, that'd be appreciated. I've taken a slice perpendicular to the axis of rotation. If you want to compute this volume through the shell method, what you should compute is:$$2\pi\int_0^4y\left(2\sqrt y+y\right)\,\mathrm dy=\frac{1\,408}{15}\pi. Volume by Rotating the Area Enclosed Between 2 Curves. y=2 sin(x), y=2008(*). ' and find homework help for other Math questions at eNotes. Question Asked Aug 30, 2020. asked by me on October 31, 2010. To find the volume of the solid of revolution obtained by revolving the region bounded by : The equations {eq}y = x^2 {/eq}, the tangent line to this equation at {eq}x = -1\Rightarrow y=-2x-1 {/eq},. Find the volume V obtained by rotating the region bounded by the curves about the given axis. Then find the area of the region. Look at the first example on the last page here and try using the washer method. y2 = 2x, x = 2y; about the y-axis V= Sketch the region. Decide whether to integrate with respect to x or y. Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves y=x^2 and y^2=x about the x-axis. The curve on the left (y = sqrtx) is x = y^2 on the right is the line x = y Rotating the slice will generate a washer of thickness dy and volume pi(R^2. Find the volume of the solid obtained by rotating the region bounded by the curves y = SQRT(x), x = 2 and y = 0 about the x-axis. 0 05 05 10 1. 0 0 Sketch the sold, and a typical disk or washer. Sketch the region, the solid, and a typical disk or washer. How do you find the volume of the solid generated by revolving the region bounded by the graph What is the volume of the region enclosed by #y=2-0. y = x + 1, y = 0, x = 0, x = 2; about the x-axis V = Sketch the region. The slice is taken at a value of y, so we need to rewrite the curve y=sqrt(x-1) as x = y^2+1 The thickness of the slice and the shell is dy The radius is r = 7-y The height is h = 5-(y^2+1) = 4-y^2 The shell has volume 2pirhxx"thickness" = 2pi(7-y)(4-y^2)dy y varies from 0. 5 OO -ast 1. 5 Sketch the sold, and a typical disk or washer. y = sin(x), y = 0, π/2 ≤ x ≤ π; about the x−axis 2. In questions 2, 3 and 5, give the answers in exact form (not a decimal approximation). Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis. Find the volume of the solid obtained by rotating the region bounded by the graphs of the given expressions about the specified line. Image Transcriptionclose. Volume by Rotating the Area Enclosed Between 2 Curves. Find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis. Decide whether to integrate with respect x to y or. Find the volume of the solid obtained by rotating the region bounded by y? = x + 4 and 6 - x about the line y = -6 by using: 3 a) The method of Cylindrical Shells. y2 = 2x, x = 2y; about the y-axis V= Sketch the region. Then find the area of the region. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. region, the solid, and a typical disk or washer. Get an answer for 'y = 1 + sec(x), y = 3` Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. sketch the region, the solid, and a typical disk or washer. y2 = 2x, x = 2y; about the y-axis V= Sketch the region. y = 1/x, y = 0, x = 1, x = 4; about the x-axis. When a two-dimensional region is revolved about an axis lying in the same plane, a solid volume is obtained. Answer to: Find the volume of the solid of revolution formed by rotating the region bounded by y = cos(x) and y = sin(2x) around the y-axis. asked • 08/23/15 find the volume of the solid obtained by rotating the region bounded by xy=4 and y=(x-3)^2 about the x-axis. y=2 sin(x), y=2008(*). The thickness of the slice is dy, so we need the equations in the form x = a function of y. Then use your calculator to evaluate the integral correct to five decimal places. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y 15 10 5 X х 2 4 6 8 2 4 6 8 O у 15 3 10 J 2 1 х 2 4 6 8 2 4 6 8 Sketch the solid, and a typical disk or washer. Not entirely sure where to start?. The curve on the left (y = sqrtx) is x = y^2 on the right is the line x = y Rotating the slice will generate a washer of thickness dy and volume pi(R^2. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. у 10 6 8 4 4 2 21 х -5 LO -5 5. The curve on the left (y = sqrtx) is x = y^2 on the right is the line x = y Rotating the slice will generate a washer of thickness dy and volume pi(R^2. Sketch the region, the solid, and a.