JEE Main 2025 (Online) 28th January Morning ShiftQuestion 1
The area (in sq. units) of the region
$\{(x,y): 0\le y\le 2|x|+1,\ 0\le y\le x^2+1,\ |x|\le 3\}$ is
Application of Integrals
Solution
For $x\ge0$, $x^2+1\le2x+1$ on $[0,2]$ and $2x+1\le x^2+1$ on $[2,3]$. Area $=2\left[\int_0^2(x^2+1)dx+\int_2^3(2x+1)dx\right]=2\left[\frac{14}{3}+6\right]=\frac{64}{3}$.