A) 0
B) \[-2\log (a+10)\]
C) \[2\log \left( \frac{a+10}{a-10} \right)\]
D) \[2\log (a+10)\]
E) \[2\]
Correct Answer: A
Solution :
\[\int_{-10}^{10}{\log \left( \frac{a+x}{a-x} \right)}dx\] 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 \[\therefore \] \[\int_{-10}^{10}{f(x)}dx=0\]
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