Question

Area bounded by $y=f^{-1}\left(x\right)$ and tangent and normal drawn to it at the points with abscissae $\pi$ and $2\pi$, where f(x) = sinx - x is

• A. $\frac{{\pi }^2}{2}-1$
• B. $\frac{{\pi }^2}{2}-2$
• C. $\frac{{\pi }^2}{2}-3$
• D. $\frac{{\pi }^2}{2}-4$

Answer 1

The correct option is B $\frac{{\pi }^2}{2}-2$

Required area $A={\int }_{\pi }^{2\pi }\left(\right(sinx-x)+2\pi )dx=\frac{{\pi }^2}{2}-2sq.units$