JEE Main 2025 (Online) 7th April Morning ShiftQuestion 1
If the area of the region bounded by the curves $y=4-\frac{x^{2}}{4}$ and $y=\frac{x-4}{2}$ is equal to $\alpha$, then $6\alpha$ equals
Application of Integrals
Solution
Intersection: $4-\frac{x^2}{4}=\frac{x-4}{2}\Rightarrow x^2+2x-24=0$, $x=-6,4$. $\alpha=\int_{-6}^{4}\left(6-\frac x2-\frac{x^2}{4}\right)dx=\frac{125}{3}$. $6\alpha=250$. Option (D).