JEE Main 2024 (Online) 4th April Evening ShiftQuestion 1
The area (in sq. units) of the region described by $\left\{(x,y):y^{2}\le2x,\ \text{and}\ y\ge4x-1\right\}$ is
Application of Integrals
Solution
In terms of $y$ the region is $\frac{y^2}2\le x\le\frac{y+1}4$, and the curves meet at $y=-\frac12,1$. Area $=\int_{-1/2}^{1}\left(\frac{y+1}4-\frac{y^2}2\right)dy=\frac{9}{32}$.