Question

The area bounded by $y=x^2,x=y^2$ is

• A. $1$
• B. $\frac{1}{6}$
• C. $\frac{3}{4}$
• D. $Noneofthese$

Answer 1

The correct option is A $1$

$y=x^2{y}^2=x⟹y=\sqrt{x}$

The curves intersect at $(0,0)$ and $(1,1)$

Area between the curves is given by

${\int }_0^1\sqrt{x}-x^{2}dx{\frac{2}{3}{x}^{3/2}+\frac{x^3}{3}|}_0^1\frac{2}{3}+\frac{1}{3}=1$