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

Explanation

To solve the integral \( I = \int_{0}^{2} x \sqrt{2 - x} \, dx \), we can utilize a property of definite integrals. This property states that if we have an integral from \( 0 \) to \( a \) of a function \( f(x) \), we can express it in another form by substituting \( a - x \) into the function.

### Step-by-Step Solution

1. **Set up the integral:**
\[ I = \int_{0}^{2} x \sqrt{2 - x} \, dx \]
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