Area bounded by `y = |x - pi/2|` and `x = 0, x = pi` equals

Options

A. `pi//2`
B. `pi^(2)//4`
C. `pi^(2)//8`
D. 0

Answer

To find the area bounded by the curve \( y = |x - \frac{\pi}{2}| \) and the lines \( x = 0 \) and \( x = \pi \), we can follow these steps:

### Step 1: Understand the function
The function \( y = |x - \frac{\pi}{2}| \) represents a V-shaped graph that has a vertex at \( x = \frac{\pi}{2} \). The function can be broken down into two linear pieces:
- For \( x < \frac{\pi}{2} \), \( y = \frac{\pi}{2} - x \)
- For \( x \geq \frac{\pi}{2} \), \( y = x - \frac{\pi}{2} \)