Q. $\int_{- 10}^{10}{\log\left( \frac{a + x}{a - x} \right)}dx$ is equal to
A) 0
B) $- 2\ \log(a + 10)$
C) $2\log\left( \frac{a + 10}{a - 10} \right)$
D) $2\ \log(a + 10)$
Explanation
(a)
Let $f(x) = \log\left( \frac{a + x}{a - x} \right)$
$\Rightarrow f( - x) = \log\left( \frac{a - x}{a + x} \right)$
$= - \log\left( \frac{a + x}{a - x} \right)$
$= - f(x)$
$\Rightarrow f(x)$ is an odd function.
$\therefore\int_{- 10}^{10}{f(x)dx = 0}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.