Question

The area (in sq. units) of the region $\left\{\right(x,y):y^2\ge 2xand{x}^2+y^2\le 4x,x\ge 0,y\ge 0\}$ is :

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$Area=\frac{\pi 2^2}{4}-{\int }_0^2\sqrt{2x}dx=\pi -\sqrt{2}.\frac{2}{3}{x}^{\frac{3}{2}}{|}_0^2=\pi -\frac{8}{3}$