Find the area bounded by curves


Find the area bounded by curves $\left\{(x, y): y \geq x^{2}\right.$ and $\left.y=|x|\right\}$


The area bounded by the curves, $\left\{(x, y): y \geq x^{2}\right.$ and $\left.y=|x|\right\}$, is represented by the shaded region as

It can be observed that the required area is symmetrical about y-axis.

Required area $=2[$ Area $($ OCAO $)-$ Area $($ OCADO $)]$

$=2\left[\int_{0}^{1} x d x-\int_{0}^{1} x^{2} d x\right]$



$=2\left[\frac{1}{6}\right]=\frac{1}{3}$ units



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