# Arc length (mostly a problem with integration)

1. Feb 2, 2009

### Geekchick

1. The problem statement, all variables and given/known data

Find the arc length oh the graph f(x)=cosx on the integral [0,$$\frac{\pi}{2}$$]

2. Relevant equations

$$\int^{b}_{a}$$$$\sqrt{1+{f'(x)}^{2}}$$dx

3. The attempt at a solution

Alright so I took the derivative of f(x) to get f'(x)=-sinx then I squared it to get sin$$^{2}$$x so I could plug it into the formula to get $$\int^{\frac{\pi}{2}}_{0}$$$$\sqrt{1+sin^{2}x}$$ the problem is when I try to integrate...well i can't. I tried to use substitution but since i don't have cos$$^{2}$$x anywhere I had some issues.

2. Feb 2, 2009

### Geekchick

Anybody? Please this is driving me crazy!

3. Feb 2, 2009

### djeitnstine

You can't do it. You have to do a numerical approximation

4. Feb 2, 2009

### djeitnstine

I get 1.910098938245763 with wxmaxima