JEE Main 2024 (Online) 5th April Evening ShiftQuestion 1
The area enclosed between the curves $y=x|x|$ and $y=x-|x|$ is :
Application of Integrals
Solution
For $x\ge0$ both curves give $y=x^2$ and $y=0$, meeting only at $0$. For $x<0$: $y=-x^2$ and $y=2x$ meet at $x=-2$. Area $=\int_{-2}^0(-x^2-2x)\,dx=\frac43$.