91Ó°ÊÓ

For the following exercises, use shells to find the volume generated by rotating the regions between the given curve and y = 0 around the x-axis. $$x=\frac{1+y^{2}}{y}, y=0, \text { and } y=2$$

For the following exercises, use shells to find the volume generated by rotating the regions between the given curve and \(y=0\) around the \(x\) -axis. \(x=\cos y, y=0,\) and \(y=\pi\).

For the following exercises, use shells to find the volume generated by rotating the regions between the given curve and y = 0 around the x-axis. \(x=y^{3}-4 y^{2}, x=-1,\) and \(x=2\)

For the following exercises, find the volume generated when the region between the curves is rotated around the given axis. y = 3 ? x, y = 0, x = 0, and x = 2 rotated around the y-axis.

For the following exercises, find the volume generated when the region between the curves is rotated around the given axis. \(\quad y=x^{3}, y=0,\) and \(y=8\) rotated around the \(y\) -axis.

For the following exercises, find the volume generated when the region between the curves is rotated around the given axis. \(y=x^{2}, y=x,\) rotated around the \(y\) -axis.

For the following exercises, find the volume generated when the region between the curves is rotated around the given axis. \(y=\sqrt{x}, x=0,\) and \(x=1\) rotated around the line \(x=2\)

For the following exercises, find the volume generated when the region between the curves is rotated around the given axis. \(y=\frac{1}{4-x}, x=1,\) and \(x=2\) rotated around the line \(x=4\)

For the following exercises, find the volume generated when the region between the curves is rotated around the given axis. \(y=\sqrt{x}\) and \(y=x^{2}\) rotated around the \(y\) -axis.

For the following exercises, find the volume generated when the region between the curves is rotated around the given axis. \(y=\sqrt{x}\) and \(y=x^{2}\) rotated around the line \(x=2\)