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JEE Mains · Maths · STD 12 - 8. Application and integration
\(\int \limits_{-\pi}^{\pi}|\pi-| x || d x\) is equal to :
- A \(\pi^{2}\)
- B \(2 \pi^{2}\)
- C \(\sqrt{2} \pi^{2}\)
- D \(\frac{\pi^{2}}{2}\)
Answer & Solution
Correct Answer
(A) \(\pi^{2}\)
Step-by-step Solution
Detailed explanation
\(\int_{-\pi}^{\pi}|\pi-| x || d x =2 \int_{0}^{\pi}|\pi- x | d x\) \(=2 \int_{0}^{\pi}(\pi- x ) d x\) \(=2\left[\pi x -\frac{ x ^{2}}{2}\right]_{0}^{\pi}=\pi^{2}\)
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