Integral over 2 pi of Cosine of n x

Theorem
Let $m \in \Z$ be an integer.

Then:


 * $\displaystyle \int_0^{2 \pi} \cos m x \, \mathrm d x = \begin{cases} 0 & : m \ne 0 \\ 2 \pi & : m = 0 \end{cases}$

Proof
Let $m \ne 0$.

Let $m = 0$.