Mathematics - Area Under Curves Question with Solution | TestHub

Away from the isolated points where $\sin x=0,\left[-{\sin }^{2}x\right]=-1$, so the second curve is $y={\sec }^{-1}(-1)=$ $\pi$. The isolated undefined points do not affect area. The intersections with $y=x^2$ are $x=\pm \sqrt{\pi }$, hence area $={\int }_{-\sqrt{\pi }}^{\sqrt{\pi }}\left(\pi -x^2\right)dx=\frac{4}{3}\pi \sqrt{\pi }$.