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 _____.

$$A = \int_{-1}^{0} (x^2 - 3x)dx + \int_{0}^{2} (3x - x^2) dx$$

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

$$\Rightarrow A = \frac{11}{6} + \frac{10}{3} = \frac{31}{6}$$

$$\therefore 12A = 62$$