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

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

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

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