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

• A

  $\frac{5}{3}$ sq. units
• B

  $\frac{5}{4}$ sq. units
• Correct answer
  C

  $\frac{5}{12}$ sq. unit
• D

  $\frac{12}{5}$ sq. units

Solution

Given curves are $y=x^3$ and $y=\sqrt{x}$ Both curves intersects at $x=0$ and $x=1$ Shaded region is required area $\begin{aligned} A & =\left|\int_0^1\left(x^3-\sqrt{x}\right) d x\right|=\left|\left[\frac{x^4}{4}-\frac{2 x^{3 / 2}}{3}\right]_0^1\right| \\ & =\left|\left[\frac{1}{4}-\frac{2}{3}\right]\right| \\ & =\frac{5}{12} \text { sq. unit } \end{aligned}$

Hence, the correct answer is option: 'C'.