Question

Let $A$ be the area bounded by the curve $y=x|x-3|$, the $x$-axis and the ordinates $x=-1$ and $x=2$. Then $12 A$ is equal to. _____

Answer 1

$ A =\int\limits_{-1}^0\left( x ^2-3 x \right) dx +\int \limits_0^2\left(3 x - x ^2\right) dx $
$ \Rightarrow A =\frac{ x ^3}{3}-\left.\frac{3 x ^2}{2}\right|_{-1} ^0+\frac{3 x ^2}{2}-\left.\frac{ x ^3}{3}\right|_0 ^2 $
$\Rightarrow A =\frac{11}{6}+\frac{10}{3}=\frac{31}{6} $
$ \therefore 12 A =62$