Q. The area bounded by the parabolas $y = {4x}^{2},y = \frac{x^{2}}{9}$ and the line $y = 2\$is
A) $\frac{5\sqrt{2}}{3}\ sq\ units$
B) $\frac{10\sqrt{2}}{3}\ sq\ units$
C) $\frac{15\sqrt{2}}{3}\ sq\ units$
D) $\frac{20\sqrt{2}}{3}\ sq\ units$
Explanation
(d)
$Required\ area = 2\int_{0}^{2}{\left( 3\sqrt{y} - \frac{\sqrt{y}}{2} \right)dy}$
$= 2\int_{0}^{2}{\left( \frac{5\sqrt{y}}{2} \right)dy = 5(y^{3/2})_{0}^{2}\ \frac{2}{3}}$
$= \frac{10}{3}(\sqrt{8} - 0)$
$= \frac{20\sqrt{2}}{3}\ sq\ units$
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Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.