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int(0)^(1)sin^(-1)sqrt(x)dx...

`int_(0)^(1)sin^(-1)sqrt(x)dx`

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To solve the integral \( I = \int_{0}^{1} \sin^{-1}(\sqrt{x}) \, dx \), we will use a substitution method. Here are the steps: ### Step 1: Substitution Let \( t = \sin^{-1}(\sqrt{x}) \). Then, we have: \[ \sqrt{x} = \sin(t) \implies x = \sin^2(t) \] ...
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