91Ó°ÊÓ

For the following exercises, find the lengths of the functions of y over the given interval. If you cannot evaluate the integral exactly, use technology to approximate it. $$x=\sqrt{y} \text { from } y=0 \text { to } y=1$$

For the following exercises, find the lengths of the functions of y over the given interval. If you cannot evaluate the integral exactly, use technology to approximate it. $$x=\frac{2}{3}\left(y^{2}+1\right)^{3 / 2} \text { from } y=1 \text { to } y=3$$

For the following exercises, find the lengths of the functions of y over the given interval. If you cannot evaluate the integral exactly, use technology to approximate it. $$x=\tan y \text { from } y=0 \text { to } y=\frac{3}{4}$$

For the following exercises, find the lengths of the functions of \(y\) over the given interval. If you cannot evaluate the integral exactly, use technology to approximate it. [T] \(x=\cos ^{2} y\) from \(y=-\frac{\pi}{2}\) to \(y=\frac{\pi}{2}\).

For the following exercises, find the lengths of the functions of y over the given interval. If you cannot evaluate the integral exactly, use technology to approximate it. $$x=4^{y} \text { from } y=0 \text { to } y=2$$

For the following exercises, find the lengths of the functions of y over the given interval. If you cannot evaluate the integral exactly, use technology to approximate it. $$x=\ln (y) \text { on } y=\frac{1}{e} \text { to } y=e$$

For the following exercises, find the surface area of the volume generated when the following curves revolve around the \(x\) -axis. If you cannot evaluate the integral exactly, use your calculator to approximate it. $$y=\sqrt{x} \text { from } x=2 \text { to } x=6$$

For the following exercises, find the surface area of the volume generated when the following curves revolve around the \(x\) -axis. If you cannot evaluate the integral exactly, use your calculator to approximate it. $$y=x^{3} \text { from } x=0 \text { to } x=1$$

For the following exercises, find the surface area of the volume generated when the following curves revolve around the \(x\) -axis. If you cannot evaluate the integral exactly, use your calculator to approximate it. $$y=7 x \text { from } x=-1 \text { to } x=1$$

For the following exercises, find the surface area of the volume generated when the following curves revolve around the \(x\) -axis. If you cannot evaluate the integral exactly, use your calculator to approximate it. $$y=\frac{1}{x^{2}} \text { from } x=1 \text { to } x=3$$