Area of the region enclosed by the curves y=√x and y=x^2 is :

The correct answer is Option (2) - $\frac{1}{3}$ units²

at $\sqrt{x}=x^2$

$x=0,1$ point of intersection

area = $\int\limits_0^1\sqrt{x}-x^2dx$

$=\left[\frac{2}{3}x\sqrt{x}-\frac{x^3}{3}\right]_0^1=\frac{1}{3}unit^2$