Question

The area bounded by the two curves $y=\sqrt{x}$ and $x=\sqrt{y}$ is:

• A. $\frac{1}{3}$ sq, units
• B. $\frac{2}{3}$ sq. units
• C. $\frac{1}{5}$ sq. units
• D. $\frac{1}{7}$ sq. units

Answer 1

Answer: (A)

$\frac{1}{3}$ sq, units

$y=\sqrt{x}$ and $x=\sqrt{y}$
Area $=\stackrel{1}{\underset{0}{\int }}(\sqrt{x}-x^2)dx$
$=\frac{2}{3}\left(1\right)-1/3=1/3squnits$