91Ó°ÊÓ

For the following exercises, find the lengths of the functions of \(x\) over the given interval. If you cannot evaluate the integral exactly, use technology to approximate it. $$ y=\frac{1}{3}\left(x^{2}+2\right)^{3 / 2} \text { from } x=0 \text { to } x=1 $$

For the following exercises, find the lengths of the functions of \(x\) over the given interval. If you cannot evaluate the integral exactly, use technology to approximate it. $$ [\mathrm{T}] y=e^{x} \text { on } x=0 \text { to } x=1 $$

For the following exercises, find the lengths of the functions of \(x\) over the given interval. If you cannot evaluate the integral exactly, use technology to approximate it. $$ y=\frac{x^{3}}{3}+\frac{1}{4 x} \text { from } x=1 \text { to } x=3 $$

For the following exercises, find the lengths of the functions of \(x\) over the given interval. If you cannot evaluate the integral exactly, use technology to approximate it. $$ y=\frac{x^{4}}{4}+\frac{1}{8 x^{2}} \text { from } x=1 \text { to } x=2 $$

For the following exercises, find the lengths of the functions of \(x\) over the given interval. If you cannot evaluate the integral exactly, use technology to approximate it. $$ y=\frac{2 x^{3 / 2}}{3}-\frac{x^{1 / 2}}{2} \text { from } x=1 \text { to } x=4 $$

For the following exercises, find the lengths of the functions of \(x\) over the given interval. If you cannot evaluate the integral exactly, use technology to approximate it. $$ [\mathrm{T}] y=\sin x \text { on } x=0 \text { to } x=\pi $$

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

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

Find the lengths of the functions of \(y\) over the given interval. If you cannot evaluate the integral exactly, use technology to approximate it. $$ \text { [T] } x=y^{2} \text { from } y=0 \text { to } y=1 $$

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