Arc Length Need Verification, If Wrong, Can You Help?

[zcabral]

Homework Statement

Length of curve: y=1/2(ex-e-x) from 0 to 2

Homework Equations

s = ∫√[1+(dy/dx)^2] dx

The Attempt at a Solution

[sqrt(4+2e^(-x)+e^x)]*[-1+e^x]/[1+e^x].
= 3.323971

 

[Hootenanny]

Your notation is ambiguous. I'm guessing that your curve is,

$$y(x) = \frac{e^x-e^{-x}}{2}$$

In which case it may be useful to note that,

$$\frac{e^x-e^{-x}}{2} = \sinh(x)$$

Which (along with a hyperbolic identity) would greatly simplify your integrand.