JEE Main 2024 (Online) 30th January Morning ShiftQuestion 1
The area (in square units) of the region bounded by the parabola $y^{2}=4(x-2)$ and the line $y=2x-8$, is :
Application of Integrals
Solution
Line: $x=\tfrac y2+4$; parabola: $x=2+\tfrac{y^2}4$. Equal: $y^2-2y-8=0\Rightarrow y=-2,4$. Area $=\int_{-2}^4\left(\tfrac y2+2-\tfrac{y^2}4\right)dy=\left[\tfrac{y^2}4+2y-\tfrac{y^3}{12}\right]_{-2}^4=\tfrac{20}3+\tfrac73=9$. Answer: (D).