Hi guys I'm looking to evaluate the following integral. Would someone be able to help me? I'm desperate, it is for an exam.
The integral I have to evaluate is as follows: $$\int_{-\infty}^{+\infty}\omega|\hat{G}(\omega)|^2 \, d\omega $$
where the function G(x) is : $$ G(x) = \begin{cases} 2-\frac{2x^2}{\pi^2} & -\pi<x \leq0 \\ cosx+1 & 0<x \leq \pi \end{cases} $$ I am aware that the integral vanishes.
Thanks all.