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} $ .