91Ó°ÊÓ

For the following exercises, draw the region bounded by the curves. Then, use the disk method to find the volume when the region is rotated around the \(x\) -axis. $$ y=\frac{1}{x}, x=2, \text { and } y=3 $$

For the following exercises, draw the region bounded by the curves. Then, use the disk method to find the volume when the region is rotated around the \(x\) -axis. $$ x^{2}-y^{2}=9 \text { and } x+y=9, y=0 \text { and } x=0 $$

For the following exercises, draw the region bounded by the curves. Then, find the volume when the region is rotated around the \(y\) -axis. $$ y=4-\frac{1}{2} x, x=0, \text { and } y=0 $$

For the following exercises, draw the region bounded by the curves. Then, find the volume when the region is rotated around the \(y\) -axis. $$ y=2 x^{3}, x=0, x=1, \text { and } y=0 $$

For the following exercises, draw the region bounded by the curves. Then, find the volume when the region is rotated around the \(y\) -axis. $$ y=3 x^{2}, x=0, \text { and } y=3 $$

For the following exercises, draw the region bounded by the curves. Then, find the volume when the region is rotated around the \(y\) -axis. $$ y=\sqrt{4-x^{2}}, y=0, \text { and } x=0 $$

For the following exercises, draw the region bounded by the curves. Then, find the volume when the region is rotated around the \(y\) -axis. $$ y=\frac{1}{\sqrt{x+1}}, x=0, \text { and } x=3 $$

For the following exercises, draw the region bounded by the curves. Then, find the volume when the region is rotated around the \(y\) -axis. $$ x=\sec (y) \text { and } y=\frac{\pi}{4}, y=0 \text { and } x=0 $$

For the following exercises, draw the region bounded by the curves. Then, find the volume when the region is rotated around the \(y\) -axis. $$ y=\frac{1}{x+1}, x=0, \text { and } x=2 $$

For the following exercises, draw the region bounded by the curves. Then, find the volume when the region is rotated around the \(y\) -axis. $$ y=4-x, y=x, \text { and } x=0 $$