The area bounded by the curve `y = cos^-1(cos x)` and `y=|x-pi|` is

Options

A. (a)`pi^(2)` sq. unit
B. (b)`2pi^(2)` sq. unit
C. (c)`(pi^(2))/(2)` sq. unit
D. (d)`(pi^(2))/(4)` sq. unit

Answer

To find the area bounded by the curves \( y = \cos^{-1}(\cos x) \) and \( y = |x - \pi| \), we will follow these steps:

### Step 1: Understand the curves

The curve \( y = \cos^{-1}(\cos x) \) simplifies to:
- \( y = x \) for \( 0 \leq x < \pi \)
- \( y = 2\pi - x \) for \( \pi < x < 2\pi \)

The curve \( y = |x - \pi| \) can be expressed as:
- \( y = x - \pi \) for \( x \geq \pi \)
- \( y = \pi - x \) for \( x < \pi \)