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STD 12 - 8. Application and integration — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 8. Application and integration4 Marks
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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