**Question: **$\int_{-\pi}^{\pi}|\pi-| x|| d x$ is equal to :

$\pi^{2}$

$2 \pi^{2}$

$\sqrt{2} \pi^{2}$

$\frac{\pi^{2}}{2}$

Correct Option: 1

**Solution:**
$\int_{-\pi}^{\pi}|\pi-| x|| d x=2 \int_{0}^{\pi}|\pi-x| d x$

$=2 \int_{0}^{\pi}(\pi-x) d x$

$=2\left[\pi x-\frac{x^{2}}{2}\right]_{0}^{\pi}=\pi^{2}$