Question

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

• A. $\frac{1}{3}$
• B. $\frac{1}{2}$
• C. $\frac{2}{4}$
• D. $3$

Answer 1

The correct option is A $\frac{1}{3}$

The graph is shown in the image.

The intersection points of $y=x^2$ and $x=y^2$ are $(0,0)$ and $(1,1)$.

Now, $A={\int }_0^1[\sqrt{x}]-{\int }_0^1[x^2]$

$A=[\frac{2(x{)}^{\frac{3}{2}}}{3}]{|}_0^1-[\frac{x^2}{2}]{|}_0^1$

$A=\frac{2}{3}-\frac{1}{3}$ sq.unit

$A=\frac{1}{3}$ sq.unit