The value of `int_(2pi)^(0) min{|x-pi|, cos^(-1)(cosx)} dx` is -

Options

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

Answer

B

Explanation

`I=underset(pi//2)overset(0)intxdx + underset(pi//2)overset(pi)(int)(pi-x)dx + underset(pi)overset(3pi//2)(int)(x-pi)dx+underset(3pi//2)overset(2pi)int2pi - xdx`
`(pi^(2))/(8)+(pi^(2))/(8)+(pi^(2))/(8)+(pi^(2))/(8)=(pi^(2))/(2)`