Question

The area of the region bounded by the curve $y=x^2$ and $y={\text{sec}}^{-1}[-{\text{sin}}^{2}x]$, (where [.] denotes the greatest integer function), is

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

Answer 1

The correct option is B

$\frac{4}{3}\pi \sqrt{\pi }$

$[-{\text{sin}}^{2}x]=0$ or -1 but ${\text{sec}}^{-1}\left(0\right)$ is not defined.

$\Rightarrow$ The required area $={\int }_{-\sqrt{\pi }}^{\sqrt{\pi }}(\pi -x^2)dx=\frac{4}{3}\pi \sqrt{\pi }$