A) \[0\]
B) \[1\]
C) \[\frac{1}{2}\]
D) \[-\frac{1}{2}\]
Correct Answer: A
Solution :
Given, \[f(x)={{\log }_{e}}(1+x)-{{\log }_{e}}(1-x)\] \[\therefore \] \[f(-x)={{\log }_{e}}(1-x)-{{\log }_{e}}(1+x)\] \[=-[{{\log }_{e}}(1+x)-{{\log }_{e}}(1-x)]\] \[=-f(x)\] \[\therefore \] \[f(x)\] is an odd function. \[\therefore \] \[\int_{-1/2}^{1/2}{f(x)\,dx=0}\]You need to login to perform this action.
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