91Ó°ÊÓ

For the following exercises, draw the region bounded by the curves. Then, find the volume when the region is rotated around the \(x\) -axis. $$ y=x+2, y=x+6, x=0, \text { and } x=5 $$

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

For the following exercises, draw the region bounded by the curves. Then, find the volume when the region is rotated around the \(x\) -axis. $$ \text { [T] } y=\cos x, y=e^{-x}, x=0, \text { and } x=1.2927 $$

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

For the following exercises, draw the region bounded by the curves. Then, find the volume when the region is rotated around the \(x\) -axis. $$ y=\sin x, y=5 \sin x, x=0 \text { and } x=\pi $$

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

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

For the following exercises, draw the region bounded by the curves. Then, use the washer method to find the volume when the region is revolved around the \(y\) -axis. $$ y=\sqrt[3]{x} \text { and } y=x^{3} $$

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

For the following exercises, draw the region bounded by the curves. Then, use the washer method to find the volume when the region is revolved around the \(y\) -axis. $$ x=\sqrt{9-y^{2}}, x=e^{-y}, y=0, \text { and } y=3 $$