What is integration of sin inverse cos x ?

Solution :

We have, I = \(\int\) \(sin^{-1}(cos x)\) dx

By using integration formula, cos x = \(sin({\pi\over 2} – x)\)

I = \(\int\) \(sin^{-1}[sin({\pi\over 2} – x)]\) dx

I = \(\int\) \(({\pi\over 2} – x)\) dx

I = \({\pi\over 2}x\) – \(x^2\over 2\) + C


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