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int(0)^(2) xsqrt(2-x)dx...

`int_(0)^(2) xsqrt(2-x)dx`

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To solve the integral \( I = \int_{0}^{2} x \sqrt{2 - x} \, dx \), we will use the substitution method. Here are the steps: ### Step 1: Substitution Let \( t = 2 - x \). Then, differentiate both sides to find \( dx \): \[ dx = -dt \] ...
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