Q. The value of $\int_{- 1}^{1}{\log\left( \frac{x - 1}{x + 1} \right)dx}\$is
A) 1
B) 2
C) 0
D) 4
Explanation
(c)
Let $f(x) = \log\left( \frac{x - 1}{x + 1} \right)$
$f( - {x) = log}{\left( \frac{- x - 1}{- x + 1} \right) = - \log\left( \frac{x - 1}{x + 1} \right)}$
$= - f(x)$
$\Rightarrow f(x)$is an odd function
$\therefore\ \int_{- 1}^{1}{\log{\left( \frac{x - 1}{x + 1} \right)dx = 0}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.