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:
$\int_{-\pi}^{\pi}|\pi-| x|| d x=2 \int_{0}^{\pi}|\pi-x| d x$
$=2 \int_{0}^{\pi}(\pi-x) d x$
$=2\left[\pi x-\frac{x^{2}}{2}\right]_{0}^{\pi}=\pi^{2}$
