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.

Question

#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.

Image Transcription

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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