Find the area between the curves

The required area is represented by the shaded area OBAO as

The points of intersection of the curves, $y=x$ and $y=x^{2}$, is $\mathrm{A}(1,1)$.

We draw AC perpendicular to x-axis.

∴ Area (OBAO) = Area (ΔOCA) – Area (OCABO) … (1)

$=\int_{0}^{1} x d x-\int_{0}^{1} x^{2} d x$

$=\left[\frac{x^{2}}{2}\right]_{0}^{1}-\left[\frac{x^{3}}{3}\right]_{0}^{1}$

$=\frac{1}{2}-\frac{1}{3}$

$=\frac{1}{6}$ units