Question

Find the area bounded by curves{$(x,y):y≥x^2$ and $y=|x|$}

Answer 1

The correct answer is:$\frac{1}{3}units$
The area bounded by the curves,{$(x,y):y≥x^2$ and $y=|x|$}, 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)]
$=2[∫^1_0xdx-∫^1_0x^2dx]$
$=2\bigg[\bigg[\frac{x^2}{2}\bigg]^1_0-\bigg[\frac{x^3}{3}\bigg]^1_0\bigg]$
$=2[\frac{1}{2}-\frac{1}{3}]$
$=2[\frac{1}{6}]=\frac{1}{3}units$