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. \(y=\frac{1}{x}, x=2,\) 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. \(x^{2}-y^{2}=9\) and \(x+y=9, y=0\) 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. \(y=4-\frac{1}{2} x, x=0,\) 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. \(y=2 x^{3}, x=0, x=1,\) 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. \(y=3 x^{2}, x=0,\) 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. \(y=\sqrt{4-x^{2}}, y=0,\) 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. \(y=\frac{1}{\sqrt{x+1}}, x=0,\) 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. \(x=\sec (y)\) and \(y=\frac{\pi}{4}, y=0\) 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. \(y=\frac{1}{x+1}, x=0,\) 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. \(y=4-x, y=x,\) and \(x=0\)