Question

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

• A. $\frac{\pi x}{2}+c$
• B. $\frac{\pi x^2}{2}+c$
• C. $\frac{\pi x-x^2}{2}+c$
• D. $\frac{\pi x+x^2}{2}+c$

Answer 1

The correct option is C $\frac{\pi x-x^2}{2}+c$

${\text{sin}}^{-1}\left(\cos x\right)=\frac{\pi }{2}-{\text{cos}}^{-1}\left(\cos x\right)=\frac{\pi }{2}-x$

$\int {\text{sin}}^{-1}\left(\cos x\right)dx=\int (\frac{\pi }{2}-x)dx=\frac{\pi x-x^2}{2}+C$