_ - ^ | -| x || d x is equal to : - Vidyadip

MCQ

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

✓
$\pi^{2}$
B
$2 \pi^{2}$
C
$\sqrt{2} \pi^{2}$
D
$\frac{\pi^{2}}{2}$

✓

Answer

Correct option: A.

$\pi^{2}$

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

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

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

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