Question

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

• A. $\frac{1}{3}$ sq unit
• B. $\frac{1}{6}$ sq unit
• C. $\frac{2}{3}$ sq unit
• D. $1$ sq unit

Answer 1

Answer: (B)

$\frac{1}{6}$ sq unit

Given the curve $y^2=x$ and $y=|x|$
The required area is given by
${\int }_0^1(\sqrt{x}-x)dx={\left[\begin{array}{c}\frac{x^{\frac{3}{2}}}{\frac{3}{2}}-\frac{x^2}{2}\end{array}\right]}_0^1$
$=\frac{2}{3}-\frac{1}{2}=\frac{4-3}{6}-\frac{1}{6}$