Calculus

The curves intersect at $(0, 0)$ and $(1, 1)$. Area $A = \int_0^1 (\sqrt{x} - x^2) dx = \left[\frac{2}{3}x^{3/2} - \frac{x^3}{3}\right]_0^1 = \frac{2}{3} - \frac{1}{3} = \frac{1}{3} \approx 0.333$.