question_answer

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

A)  \[\frac{5}{3}\]                                  

B)  \[\frac{5}{4}\]

C)  \[\frac{5}{12}\]                               

D)  \[\frac{12}{5}\]

Correct Answer: C

Solution :

Solving \[y=\sqrt{x}\]or\[{{y}^{2}}=x,\,(y\ge 0)\] and \[y={{x}^{3}}\]we get points of intersection (0, 0) and (1, 1) \[\therefore \] Required area \[=\int_{0}^{1}{(\sqrt{x}-{{x}^{3}})dx}\]\[=\frac{5}{12}\] sq. units