Calcualte the area under the curve $y = 2\sqrt x$ included between the lines $x = 0$ and $x = 1$.

We have, $y = 2\sqrt x$
or $\quad {y^2} = 4x,x \ge 0$
The graph of above function is part of parabola lying above x-axis.
The graph is as shown in the adjacent figure.

From the figure, area of shaded region,
$A = \int_0^1 2 \sqrt x dx$

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

$= 2\left( {\frac{2}{3}} \right) = \frac{4}{3}{\rm{sq}}$. units