The area of the region enclosed by the parabolas $$y = x^2 - 5x$$ and $$y = 7x - x^2$$ is ______

$$y = x^2 - 5x$$ and $$y = 7x - x^2$$.

Intersection: $$x^2 - 5x = 7x - x^2 \Rightarrow 2x^2 - 12x = 0 \Rightarrow x = 0$$ or $$x = 6$$.

For $$0 \leq x \leq 6$$: $$7x - x^2 \geq x^2 - 5x \Rightarrow 12x - 2x^2 \geq 0$$. True.

$$ \text{Area} = \int_0^6 [(7x-x^2) - (x^2-5x)]dx = \int_0^6 (12x - 2x^2)dx $$

$$ = [6x^2 - \frac{2x^3}{3}]_0^6 = 216 - 144 = 72 $$

The answer is 72.