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. \(y=x+2, y=x+6, x=0,\) 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. \(y=x^{2}\) 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. \(x^{2}=y^{3}\) 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. \(y=4-x^{2}\) and \(y=2-x\)

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

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

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. \(y=\sqrt{x}, x=4,\) 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. \(y=x+2, y=2 x-1,\) and \(x=0\)