91Ó°ÊÓ

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

Find the lengths of the functions of \(y\) over the given interval. If you cannot evaluate the integral exactly, use technology to approximate it. $$ \text { [T] } x=\tan y \text { from } y=0 \text { to } y=\frac{3}{4} $$

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

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. $$ y=\sqrt{x} \text { from } x=2 \text { to } x=6 $$

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. $$ y=x^{3} \text { from } x=0 \text { to } x=1 $$

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. $$ y=7 x \text { from } x=-1 \text { to } x=1 $$

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. $$ \text { [T] } y=\frac{1}{x^{2}} \text { from } x=1 \text { to } x=3 $$

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. $$ y=\sqrt{4-x^{2}} \text { from } x=-1 \text { to } x=1 $$

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. $$ y=5 x \text { from } x=1 \text { to } x=5 $$

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. $$ \text { [T] } y=\tan x \text { from } x=-\frac{\pi}{4} \text { to } x=\frac{\pi}{4} $$