If the area enclosed by the curves `f(x) = cos^(-1) (cos x) and g(x) = sin^(-1) (cos x) " in " x in [9 pi//4, 15 pi//4] " is " api^(2)//b` (where a and b are coprime), then the value of b is ____

Answer

8

Explanation

We have `g(x) = sin^(-1) (cos x) = (pi)/(2) - cos^(-1) (cos x)`
Both the curve bound the regions of same area in `[(pi)/(4), (7pi)/(4)], [(9pi)/(4), (15pi)/(4)]` and so on.

`:.` Required area = Area of shaded square
`= (9pi^(2))/(8) = (a pi^(2))/(b)`
`:. a = 9 and b = 8`