454CHAPTER 6Applications of Integration23-7 Use the method of cylindrical shells to find the volumegenerated by rotating the region bounded by the given curvesabout the y-axis.3. y x, y = 0, x= 14. y x, y = 0, x= 1, x = 225. у %3D е*, у 3D0, х3D 0, х%3D 16. у 3 4х — х*, у%3D х7. y x2, y 6x - 2x28. Let V be the volume of the solid obtained by rotating aboutthe y-axis the region bounded by y = vx and y x2. FindV both by slicing and by cylindrical shells. In both casesdraw a diagram to explain your method.

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Asked Sep 16, 2019

#6

454
CHAPTER 6
Applications of Integration
2
3-7 Use the method of cylindrical shells to find the volume
generated by rotating the region bounded by the given curves
about the y-axis.
3. y x, y = 0, x= 1
4. y x, y = 0, x= 1, x = 2
2
5. у %3D е*, у 3D0, х3D 0, х%3D 1
6. у 3 4х — х*, у%3D х
7. y x2, y 6x - 2x2
8. Let V be the volume of the solid obtained by rotating about
the y-axis the region bounded by y = vx and y x2. Find
V both by slicing and by cylindrical shells. In both cases
draw a diagram to explain your method.
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454 CHAPTER 6 Applications of Integration 2 3-7 Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y-axis. 3. y x, y = 0, x= 1 4. y x, y = 0, x= 1, x = 2 2 5. у %3D е*, у 3D0, х3D 0, х%3D 1 6. у 3 4х — х*, у%3D х 7. y x2, y 6x - 2x2 8. Let V be the volume of the solid obtained by rotating about the y-axis the region bounded by y = vx and y x2. Find V both by slicing and by cylindrical shells. In both cases draw a diagram to explain your method.

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Expert Answer

Step 1

Consider the given curves.

y 4x-xyx
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y 4x-xyx

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Step 2

Now, find the intersection point of both curves

4x-r2
x
3x -x20
(3-x)x 0
x 0,3
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4x-r2 x 3x -x20 (3-x)x 0 x 0,3

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Step 3

Formula us...

dx
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dx

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