JEE Main 2023 (Online) 24th January Evening ShiftQuestion 1
If the area of the region bounded by the curves $y^{2}-2y=-x$ and $x+y=0$ is $A$, then $8A=$
Application of Integrals
Answer$36$
Solution
$x=2y-y^2$ and $x=-y$ meet at $y=0,3$. $A=\int_0^3(3y-y^2)dy=\frac{27}2-9=\frac92$, so $8A=36$.