QJEEM23Ma3ef5: JEE Main 2023 Mathematics - Class 12 JEEM23Ma3ef5 Solution: Let be the area bounded by the curve , the -axis and the…

Step-by-Step Verified Solution

$=\int\limits_{-1}^{2}\left|3 x-x^{2}\right|$

$A=\int\limits_{-1}^{0} x^{2}-3 x d x+\int\limits_{0}^{2} 3 x-x^{2} d x$

$\left.\left.=\frac{x^{3}}{3}-\frac{3 x^{2}}{2}\right]_{-1}^{0}+\frac{3 x^{2}}{2}-\frac{x^{3}}{3}\right]_{0}^{2}$

$=0-\left(\frac{-1}{3}-\frac{3}{2}\right)+\left(6-\frac{8}{3}\right)-0$

$=\frac{31}{6}$

$\therefore 12 A=62$