Q. Area include between curves $y = x^{2} - 3x + 2$ and $y = - x^{2} + 3x - 2$ is
A) $\frac{1}{6}\ sq\ unit$
B) $\frac{1}{2}sq\ unit$
C) 1 sq unit
D) $\frac{1}{3}\ sq\ unit$
Explanation
(d)
$Required\ area = 2\int_{1}^{2}{\left( {- x}^{2} + 3x - 2 \right)dx}$
$= 2\left\lbrack \frac{- x^{3}}{3} + \frac{3x^{2}}{2} - 2x \right\rbrack_{1}^{2}$
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$= 2\left\lbrack - \frac{8}{3} + 4 - \frac{7}{6} \right\rbrack = \frac{1}{3}\ sq\ unit$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.