Application of Integrals: The area (in sq. units) of the region, given by the set… | JEE Main 2021

JEE Main 2021 (Online) 25th July Morning ShiftQuestion 1

The area (in sq. units) of the region, given by the set $\{(x,y)\in\mathbf{R}\times\mathbf{R}\mid x\ge0,\ 2x^{2}\le y\le4-2x\}$ is :

Application of Integrals

$\frac{7}{3}$✓ Correct answer$\frac{8}{3}$$\frac{13}{3}$$\frac{17}{3}$

Solution

$2x^2=4-2x\Rightarrow x^2+x-2=0\Rightarrow x=1$ (for $x\ge0$). Area $=\int_0^1(4-2x-2x^2)dx=4-1-\tfrac23=\tfrac73$. Answer: (A).

Application of Integrals - JEE Mathematics question (JEE Main 2021 (Online) 25th July Morning Shift)