Integral over 2 pi of Sine of m x by Cosine of n x

Theorem
Let $m, n \in \Z$ be integers.

Then:


 * $\displaystyle \int_0^{2 \pi} \sin m x \cos n x \, \mathrm d x = 0$

Proof
Let $m \ne n$.

When $m = n$ we have: