Integrals — Class 12 Maths Solution

: Let $I = \int {{{\sin }^{ - 1}}\left( {\cos x} \right)} dx = \int {{{\sin }^{ - 1}}\left[ {\sin \left( {\cfrac{\pi }{2} - x} \right)} \right]} dx$

$= \int {\left( {\cfrac{\pi }{2} - x} \right)dx} = \cfrac{\pi }{2}\int {dx} - \int x dx = \cfrac{{\pi x}}{2} - \cfrac{{{x^2}}}{2} + C$