The area common to the curves $y=x^3$ and $y=\sqrt{x}$ is

2 4 8 None of these

None of these

$A= \int\limits_0^1\left(\sqrt{x}-x^3\right) dx$ $=\frac{2}{3}\left|x^{3 / 2}\right|_0^1-\left|\frac{x^4}{4}\right|_0^1$ $=\frac{2}{3}-\frac{1}{4}=\frac{8-3}{12}=\frac{5}{12}$