The area enclosed between the curves $y^2=x$ and $y=|x|$ is

• A

  $2 / 3$
• B

  $1$
• Correct answer
  C

  $1 / 6$
• D

  $1 / 3$

Solution

$A=\int_0^1(\sqrt{x}-x) d x$ $=\left[\frac{2}{3} x^{3 / 2}-\frac{x^2}{2}\right]_0^1$ $=\frac{2}{3}-\frac{1}{2}=\frac{1}{6}$.

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