Question

Let f(x) = x + sin x. The area bounded by $y=f^{-1}\left(x\right),y=x,xϵ[0,\pi ]$ is

• A. 1
• B. 2
• C. 3
• D. canot be found because $f^{-1}\left(x\right)$ cannot be determined

Answer 1

The correct option is B 2

The curves given by $y=x+sinx$ and $y=f^{-1}\left(x\right)$ are images of each other in the line y = x.
Hence required area = ${\int }_0^{\pi }\left(\right(x+sinx)-x)dx=-[cosx{]}_0^{\pi }=2$