Q. The area bounded by the curves $y = (x - {1)}^{2},\ y = (x + 1)^{2}$ and $y = \frac{1}{4}$ is
A) $\frac{1}{3}\ sq\ unit$
B) $\frac{2}{3}\ sq\ unit$
C) $\frac{1}{4}sq\ unit$
D) $\frac{1}{5}sq\ unit$
Explanation
(a)
The points of intersection of given curves and line are
$Q\left( \frac{1}{2},\frac{1}{4} \right)and\ R\left( \frac{- 1}{2},\frac{1}{4} \right)$
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$Required\ area = 2\int_{0}^{1/2}{\left\{ (x - 1)^{2} - \frac{1}{4} \right\} dx}$
$= 2\left\{ \frac{{(x - 1)}^{3}}{3} - \frac{1}{4}x \right\}_{0}^{1/2}$
$= 2\left\{ \frac{{( - 1/2)}^{3}}{3} - \frac{1}{8} - \left( - \frac{1}{3} - 0 \right) \right\}$
$= \frac{1}{3}\ sq\ unit\$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.