QJEEM23Ma529b: JEE Main 2023 Mathematics - Class 12 JEEM23Ma529b Solution: If the area of the region bounded by the curves is A, then 8 A…

Step-by-Step Verified Solution

Area enclosed by

$\begin{aligned}& y^{2}-2 y=-x \\\\& x+y=0\end{aligned}$


Area $=\int_{0}^{3}\left(2 y-y^{2}\right)-(-y) d y$

$=\int_{0}^{3}\left(3 y-y^{2}\right) d y$

$\begin{aligned}& \left.=\frac{3 y^{2}}{2}-\frac{y^{3}}{3}\right]_{0}^{3} \\\\& =\frac{27}{2}-9 \\\\& =\frac{27-18}{2}=\frac{9}{2}=A\end{aligned}$

$8 A=\frac{9}{2} \times 8=36$ sq. units