Evaluate : `int_(0)^(pi) |cos x| dx`

Explanation

To evaluate the integral \( \int_{0}^{\pi} |\cos x| \, dx \), we can follow these steps:

### Step 1: Understand the behavior of \( \cos x \)
The function \( \cos x \) is positive on the interval \( [0, \frac{\pi}{2}] \) and negative on the interval \( [\frac{\pi}{2}, \pi] \). Therefore, we can express \( |\cos x| \) as:
\[
|\cos x| =
\begin{cases}
\cos x & \text{for } 0 \leq x \leq \frac{\pi}{2} \\
...