# Fourrier series question.

1. Nov 22, 2012

### anoncow

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

$\ f(x) = e^{|x|}$ with $x \in (-1,1)$ and f(x+2) = f(x) $\forall x$

2. Relevant equations

3. The attempt at a solution

What am I meant to do once I get to the last line? (assuming all is right up until then)

Last edited: Nov 22, 2012
2. Nov 22, 2012

### LCKurtz

Here is that last line.

$$2\int_0^1 e^x \cos(n \pi x)\,dx = \frac{2}{n \pi} \left[e^x\sin(n \pi x) \right]_0^1 - \frac{2}{n^2 \pi^2} \left[e^x\cos(n \pi x) \right]_0^1 - \frac{2}{n^2 \pi^2} \int_0^1 e^x \cos(n \pi x)$$

Treat that integral as an unknown and solve for it and, of course, put in the evaluated limits.