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$\int_{0}^{1} \frac{s i n^{- 1} x}{\sqrt{1 - x^{2}}} d x$

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π2

π24

π28

π22

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detailed solution

Correct option is C

Put sin−1⁡x=t⇒dt=11−x2dxL.L:t=sin−1⁡(0)=0U.L:t=sin−1⁡(1)=π2∫01 sin−1⁡x1−x2dx=∫0π/2 tdt=t220π/2=π28

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∫01sin−1x1−x2dx

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$\int_{0}^{1} \frac{s i n^{- 1} x}{\sqrt{1 - x^{2}}} d x$