Crazy Function!

Calculus Level 4

Function f(x) is given by\textbf{Function f(x) is given by} f(x)=0sin2xsin1tdt+0cos2xcos1tdt f(x) = \int_{0}^{sin^{2}x} \sin^{-1}\sqrt{t} dt + \int_{0}^{cos^{2}x} \cos^{-1}\sqrt{t} dt

Find\textbf{Find} f(π2)f(\sqrt{\frac{π}{2}})

x belongs in the interval [0,π/2]\textbf{x belongs in the interval [0,π/2]}

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