AP EAMCET · Maths · Definite Integration
\(\int_{-\pi / 2}^{2 \pi} \sin ^{-1}(\sin x) d x=\)
- A \(15 \pi^2 / 8\)
- B \(-\pi^2 / 8\)
- C \(-7 \pi^2 / 8\)
- D \(7 \pi^2 / 8\)
Answer & Solution
Correct Answer
(B) \(-\pi^2 / 8\)
Step-by-step Solution
Detailed explanation
\(I=\int_{-\pi / 2}^{2 \pi} \sin ^{-1}(\sin x) d x\) \(=\int_{-\pi / 2}^{\pi / 2} \sin ^{-1}(\sin x) d x+\int_{\pi / 2}^{3 \pi / 2} \sin ^{-1}(\sin x) d x\) \(+\int_{3 \pi / 2}^{2 \pi} \sin ^{-1}(\sin x) d x\)…
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