$\int {sin}^{- 1} (cos x) d x$ is equal to

\frac{π x}{2} + c

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\frac{π x^{2}}{2} + c

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\frac{π x - x^{2}}{2} + c

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\frac{π x + x^{2}}{2} + c

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Solution

The correct option is C $\frac{π x - x^{2}}{2} + c$
${sin}^{- 1} (cos x) = \frac{π}{2} - {cos}^{- 1} (cos x) = \frac{π}{2} - x$
$\int {sin}^{- 1} (cos x) d x = \int (\frac{π}{2} - x) d x = \frac{π x - x^{2}}{2} + C$

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