Confusing Step - Euler's Formula?

[BustedBreaks]

I'm following the answer to a problem and I see this step which I am unsure about:$$F[k]=\frac{1}{2}\int^{1}_{-1}|x|e^{-\pi i k x}dx$$

$$F[k]=\frac{1}{2}\int^{1}_{-1}|x|cos(\pi k x)dx$$

For k equal to all integers. Shouldn't the conversion from the exponential be $$cos(-\pi k x)$$

 

[BustedBreaks]

Crap, wrong section

 

[Mark44]

$$e^{-i \pi k x}~=~cos(- \pi k x) + i sin(- \pi k x)$$

cos(-u) = cos(u)

 

[BustedBreaks]

...Duh...

Thanks.