Q. $3a\int_{0}^{1}{\left( \frac{ax - 1}{a - 1} \right)^{2}dx}$ is equal to
A) $a - 1 + (a - 1)^{- 2}$
B) $a + a^{- 2}$
C) $a - a^{2}$
D) $a^{2} + \frac{1}{a^{2}}$
Explanation
(a)
$3a\int_{0}^{1}\left( \frac{ax - 1}{a - 1} \right)^{2}dx = \frac{3a}{(a - 1)^{2}}\left\lbrack \frac{(ax - 1)^{3}}{3} \times \frac{1}{a} \right\rbrack_{0}^{1}$
$= \frac{1}{(a - 1)^{2}}\left\lbrack (a - 1)^{3} + 1 \right\rbrack$
$= (a - 1) + (a - 1)^{- 2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.