The area of the region bounded by the parabola $y=x^2$ and the curve $y=|x|$ is

• A

  $\frac{1}{2}$ sq. units
• Correct answer
  B

  $\frac{1}{3}$ sq. units
• C

  $\frac{1}{4}$ sq. units
• D

  $\frac{1}{6}$ sq. units

Solution

$\begin{aligned} \text { Required area } & =2 \int_0^1\left(x-x^2\right) \mathrm{d} x \\ & =2\left[\frac{x^2}{2}-\frac{x^3}{3}\right]_0^1 \\ & =2\left(\frac{1}{2}-\frac{1}{3}\right)=\frac{1}{3} \text { sq.units }\end{aligned}$

Hence, the correct answer is option: 'B'.