Find the area of the region bounded by the two parabolas $y=x^2 $ and $y^2=x$ :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $\frac{1}{3}$
$y=x^2 $ and $y^2=x$
they both intersect at $x^4=x$
$⇒x=0,1$
Required area = $\int\limits_0^1\sqrt{x}-x^2dx$
$=\left[\frac{2}{3}x^{5/2}-\frac{x^3}{3}\right]_0^1=\frac{2}{3}-\frac{1}{3}=\frac{1}{3}$