If the area enclosed by the curves f(x) = ^ -1 ( x) and g(x) = ^ -1 ( x) in x [ 9 4 ,…

MATHEMATICS · Subjective · IB Diploma Programme · Mathematics: Analysis and Approaches · Geometry and Trigonometry · Geometry and Trigonometry

Problem

If the area enclosed by the curves

f(x) = \cos^{-1}(\cos x) \text{ and } g(x) = \sin^{-1}(\cos x) \text{ in } x \in \left[ \frac{9\pi}{4}, \frac{15\pi}{4} \right]

\frac{a\pi^2}{b}

(where

a

and

b

are coprime), then find

(a-b)