Question

The area of the region bounded by the curve $y=x^{2}andy=se{c}^{-1}[-si{n}^{2}x],$ (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 $\frac{4}{3}\pi \sqrt{\pi }$

$[-si{n}^{2}x]=0or-1butse{c}^{-1}\left(0\right)$ is not defined.
$\Rightarrow$ the required are $={\int }_{-\sqrt{\pi }}^{\sqrt{\pi }}(\pi -x^2)dx=\frac{4}{3}\pi \sqrt{\pi }.$