`int_(0)^(pi//2)xcosxdx` `=?`

Options

A. `(pi)/(2)`
B. `((pi)/(2)-1)`
C. `((pi)/(2)+1)`
D. none of these

Explanation

To solve the integral \( \int_{0}^{\frac{\pi}{2}} x \cos x \, dx \), we will use integration by parts.

### Step 1: Identify the parts for integration by parts
We choose:
- \( u = x \) (which we will differentiate)
- \( dv = \cos x \, dx \) (which we will integrate)

### Step 2: Differentiate and integrate
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