Originally Posted by

**Lord Voldemort** "Determine whether each integral is convergent or divergent. Evaluate those that are convergent"

$\displaystyle \int_{-\infty}^{\infty}{\cos(\pi x)}dx=\int_{-\infty}^{0}{\cos(\pi x)}dx+\int_{0}^{\infty}{\cos(\pi x)}dx$

$\displaystyle =\displaystyle\lim_{r\to-\infty}{\int_{r}^{0}{\cos(\pi x)}dx}+\displaystyle\lim_{t\to\infty}{\int_{0}^{t} {\cos(\pi x)}dx}$

Sorry people, my LaTex skills break down here. Anyways,

$\displaystyle \int{\cos(\pi x)}dx=\frac{\sin(\pi x)}{\pi}$

But then from here I have to evaluate sine to infinity...