Q. The area bounded by the curves $y = x^{3}$ and $y = x\$is
A) 1/2 $sq\ units$
B) 1/4 $sq\ units$
C) 1/8 $sq\ units$
D) 1/16 $sq\ units$
Explanation
(a)
$Required\ area = 2\int_{0}^{1}{(x - x^{3})dx}$
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$= 2\left\lbrack \frac{x^{2}}{2} - \frac{x^{4}}{4} \right\rbrack_{0}^{1} = 2\left\lbrack \frac{1}{2} - \frac{1}{4} \right\rbrack = \frac{1}{2}sq\ unit$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.