The area enclosed between the curves $y=x^{3}$ and $y=\sqrt{x}$ is, (in square units)

• A

  $\frac{5}{3}$
• B

  $\frac{5}{4}$
• Correct answer
  C

  $\frac{5}{12}$
• D

  $\frac{12}{5}$

Solution

$\begin{aligned} \text { Required area } &=\int_{0}^{1}\left(\sqrt{x}-x^{3}\right) d x \\ &=\left[\frac{2 x^{3 / 2}}{3}-\frac{x^{4}}{4}\right]_{0}^{1} \\ &=\frac{2}{3}-\frac{1}{4}=\frac{5}{12} \end{aligned}$

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