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

Correct Answer: 62

Computing the area: \[ A = \int_{-1}^{0} (x^2 - 3x) dx + \int_{0}^{2} (3x - x^2) dx \] \[ A = \left[ \frac{x^3}{3} - \frac{3x^2}{2} \right]_{-1}^{0} + \left[ \frac{3x^2}{2} - \frac{x^3}{3} \right]_{0}^{2} \] \[ A = \frac{11}{6} + \frac{10}{3} - \frac{31}{6} \] \[ \Rightarrow 12A = 62 \]