Question

Finding length of a curve describe parametrically http://i.imgur.com/8XPyk.png

I know you have to use L = integral sqrt( 1 + [f'(x)]^2). I did that but the integral looks difficult and I can't seem to find a way to solve it.
Any help is appreciated

Answer 1

\[
f(x)=\frac{1}{2}
\left(e^{-x}+e^x\right)\\
f'(x) = \frac{1}{2}
\left(e^x-e^{-x}\right)\\
1+f'(x)^2=1+\frac{1}{4}
\left(e^x-e^{-x}\right)^2 =\frac{e^{-2 x}}{4}+\frac{e^{2
x}}{4}+\frac{1}{2}=\left(\frac{1}{2}
\left(e^{-x}+e^x\right)\right)^2\\
\sqrt{1+f'(x)^2}=\frac{1}{2}
\left(e^{-x}+e^x\right)
\]
You can finish it now.