The value of the definite integral
`int_(t+2pi)^(t+5pi//2) {sin^(-1)(cosx)+cos^(-1)(cosx)}`dx is equal to

Options

A. `(pi^(2))/(2)`
B. `(pi^(2))/(8)`
C. `(pi^(2))/(4)`
D. none of these

Answer

C

Explanation

Since `sin^(-1)(cosx)+cos^(-1)(cosx)` is a periodic function with period `2pi`.
`:. I=underset(t+2pi)overset(t+5pi//2)int {sin^(-1)(cosx)+cos^(-1)(cosx)}dx`
`rArr I=underset(0)overset(pi//2)int {sin^(-1)(cosx)+cos^(-1)(cosx)}dx`
`rArr I=underset(0)overset(pi//2)int (pi)/(2)dx=(pi^(2))/(4)`