Definite Integration Question 4

Question: $ \int _{-1}^{1}{\log ( \frac{1+x}{1-x} )dx=} $

[MP PET 1995; Pb. CET 2000]

Options:

A) 2

B) 1

C) 0

D) $ \pi $

Show Answer

Answer:

Correct Answer: C

Solution:

If $ f(x)=\log ( \frac{1+x}{1-x} ), $ then $ f(-x)=\log ( \frac{1-x}{1+x} )=-f(x) $

Therefore, $ \int _{-1}^{1}{\log ( \frac{1+x}{1-x} )dx=0} $ .