Question

The area enclosed between the curves $ y=x^{3}$ and $ y=\sqrt{x} $ is

• A. $ \frac{5}{3}$ sq unit
• B. $ \frac{5}{4}$ sq unit
• C. $ \frac{5}{12}$ sq unit
• D. $ \frac{12}{5}$ sq unit

Answer 1

Answer: (C)

Solving the given curves $y=\sqrt{x}$ or $y^{2}=x$ and $y=x^{3}$

we get, the points of intersection $(0,0)$ and $(1,1)$.
$\therefore $ Required area $=\int\limits_{0}^{1}\left(\sqrt{x}-x^{3}\right) d x$
$=\left[\frac{x^{3 / 2}}{3 / 2}-\frac{x^{4}}{4}\right]_{0}^{1}$
$=\frac{5}{12}$ sq unit