Question

Area of the region bounded by two parabolas $y=x^2$ and $x=y^2$ is.

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

Answer 1

Answer: (A)

$\frac{1}{3}$

Point of intersection of both the curves are $(0,0)$ and $(1,1)$

Thus required area $=$ area of shaded region

$\left|{\int }_0^1(x^2-\sqrt{x})dx\right|=\left|{(\frac{x^3}{3}-\frac{2}{3}{x}^{3/2})}_0^1\right|$

$=|\frac{1}{3}-\frac{2}{3}|=\frac{1}{3}$ sq. units