Crazy Function!

Calculus Level 4

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

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

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

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