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)]
\(=2[∫^1_0xdx-∫^1_0x^2dx]\)
\(=2\bigg[\bigg[\frac{x^2}{2}\bigg]^1_0-\bigg[\frac{x^3}{3}\bigg]^1_0\bigg]\)
\(=2[\frac{1}{2}-\frac{1}{3}]\)
\(=2[\frac{1}{6}]=\frac{1}{3}units\)