question_answer

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)        \[\frac{12}{5}sq\,\,unit\]

Correct Answer: C

Solution :

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\[=\int_{0}^{1}{(\sqrt{x}-{{x}^{3}})}dx\]                 \[=\left[ \frac{{{x}^{3/2}}}{3/2}-\frac{{{x}^{4}}}{4} \right]_{0}^{1}\]