Q. The area of the region, enclosed by the circle $x^2 + y^2 = 2$ which is not common to the region bounded by the parabola $y^2 = x$ and the straight line $y = x$, is :
Solution:
$ A = \int^{1}_{0}\left(\sqrt{x}-x\right)dx$
$= \left[\frac{3}{2}x^{3/2} -\frac{x^{2}}{2}\right]^{1}_{0} = \frac{1}{6}$
Required Area : $\pi r^{2} -\frac{1}{6} = \frac{1}{6}\left(12\pi-1\right)$
