The area of the region(s) enclosed by the curves $y=x^2$ and $y=\sqrt{|x|}$ is

• A

  $\frac{1}{3}$
• Correct answer
  B

  $\frac{2}{3}$
• C

  $\frac{1}{6}$
• D

  1

Solution

$\begin{aligned} \text { Area } & =2 \int_0^1\left(\sqrt{x}-x^2\right) d x=2\left[\frac{2}{3}(x \sqrt{x})-\frac{x^3}{3}\right]_0^1 \\ & =2\left[\frac{2}{3}-\frac{1}{3}\right] \\ & =2 \times \frac{1}{3}=\frac{2}{3}\end{aligned}$

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