# d x is equal to :

Question:

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

1. (1) $\sqrt{2} \pi^{2}$

2. (2) $2 \pi^{2}$

3. (3) $\pi^{2}$

4. (4) $\frac{\pi^{2}}{2}$

Correct Option: , 3

Solution:

$I=\int_{-\pi}^{\pi}|\pi-| x|| d x \quad[\because|\pi-| x||$ is even $]$

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

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

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