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 $12A$ is equal to. _____

Answer 1

Answer: 62

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