Question

Find the integral of the function: ${\sin }^{-1}\left(\cos x\right)$

Answer 1

$\int {\sin }^{-1}\left(\cos x\right).dx$

$=\int {\sin }^{-1}\left[\sin (\frac{\pi }{2}-x)\right].dx$

$=\int \frac{\pi }{2}.dx-\int x.dx$

$=\frac{\pi }{2}\int 1.dx-\int x.dx$

$=\frac{\pi }{2}x-\frac{x^2}{2}+C$

Where $C$ is constant of integration.