Q. The area of the region bounced by $y^{2} = x\ and\ y = |x|$ is
A) $\frac{1}{3}\ sq\ unit$
B) $\frac{1}{6}\ sq\ unit$
C) $\frac{2}{3}\ sq\ unit$
D) 1 sq unit
Explanation
(b)
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$Required\ area = \int_{0}^{1}{\left( \sqrt{x} - x \right)dx = \left( \frac{2}{3}x^{3/2} - \frac{x^{2}}{2} \right)_{0}^{1}}$
$= \frac{2}{3} - \frac{1}{2} = \frac{4 - 3}{6} = \frac{1}{6}\ sq\ unit$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.