Evaluate the following integral: `int_0^(pi//2)x^2cos2x\ dx`

Explanation

To evaluate the integral \( I = \int_0^{\frac{\pi}{2}} x^2 \cos(2x) \, dx \), we will use integration by parts. The integration by parts formula is given by:

\[ \int u \, dv = uv - \int v \, du \]

### Step 1: Choose \( u \) and \( dv \)
Let:
...