Evaluate: `int_0^(pi//2)xsinx\ dx`

Explanation

To evaluate the integral \( \int_0^{\frac{\pi}{2}} x \sin x \, dx \), we will use the method of integration by parts.

### Step 1: Identify \( u \) and \( dv \)
Let:
- \( u = x \) (which means \( du = dx \))
- \( dv = \sin x \, dx \) (which means \( v = -\cos x \))

### Step 2: Apply the integration by parts formula
...