Q. The area enclosed between the curves $y = x^{3}$ and $y = \sqrt{x}$ is
A) $\frac{5}{3}\ sq\ units\$
B) $\frac{5}{4}sq\ units\$
C) $\frac{5}{12}\ sq\ units\$
D) $\frac{12}{5}sq\ units\$
Explanation
(c)
The point of intersection of given curves are (0,0) and (1,1).
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$\therefore Required\ area = \int_{0}^{1}{\left( \sqrt{x} - x^{3} \right)dx}$
$= \left\lbrack \frac{x^{3/2}}{3/2} - \frac{x^{4}}{4} \right\rbrack_{0}^{1}$
$= \frac{5}{12}\ sq\ unit$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.