Application of Integrals: The area (in sq. units) of the region \(x,y): y^2ge2x text and… | JEE Main 2016

JEE Main 2016 (Offline)Question 1

The area (in sq. units) of the region $\{(x,y): y^{2}\ge2x \text{ and } x^{2}+y^{2}\le4x,\ x\ge0,\ y\ge0\}$ is

Application of Integrals

$\pi-\frac{4\sqrt2}{3}$$\frac\pi2-\frac{2\sqrt2}{3}$$\pi-\frac43$$\pi-\frac83$✓ Correct answer

Solution

Curves meet at $(2,2)$; for $x>2$ the circle lies below the parabola, so area $=\int_0^2(\sqrt{4x-x^2}-\sqrt{2x})dx=\pi-\frac83$.

Application of Integrals - JEE Mathematics question (JEE Main 2016 (Offline))