# Fourier question

1. Sep 24, 2009

### Mechdude

1. The problem statement, all variables and given/known data
i was wondering why this is equal to zero : $$\int^{\pi}_{-\pi} e^{i(n+m)x }dx= 0$$ when $n\neq m$

2. Relevant equations

$$e^{inx} = cos(nx) + isin(nx)$$
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

Last edited: Sep 24, 2009
2. Sep 24, 2009

### Dick

m and n are integers, right? And I think you want (n-m) in the integral if your condition is n not equal to m. Just work out the integral to see why it's zero.

3. Sep 24, 2009

### Mechdude

Yes they are integers, and thanks for the correction it should be n-m , thanks, now anyone with links to a tutorial on why, $$\left[ \frac {e^{2nix} } {2ni} \right]^{\pi}_{-\pi} = \pi$$

Last edited: Sep 24, 2009
4. Sep 24, 2009

### Dick

e^(i*n*pi) (where n is an integer) is +1 if n is even and -1 if n is odd. e^(-i*n*pi) is that same value. I don't think you need a tutorial to prove the difference is 0.

5. Sep 24, 2009

### Mechdude

Ok, very nice thanks