JEE Main 2025 (Online) 29th January Evening ShiftQuestion 1
Let the area enclosed between the curves $|y|=1-x^{2}$ and $x^{2}+y^{2}=1$ be $\alpha$. If $9\alpha=\beta\pi+\gamma$; $\beta,\gamma$ are integers, then the value of $|\beta-\gamma|$ equals :
Application of Integrals
Solution
Curves meet at $x=0,\pm1$. Area inside the circle but outside $|y|\le1-x^2$: $\alpha=\pi-2\int_{-1}^1(1-x^2)dx=\pi-\frac83$. $9\alpha=9\pi-24$, so $|\beta-\gamma|=33$.