A) \[f(a)\]
B) \[f(2a)\]
C) \[f(0)\]
D) \[2a\]
E) \[a\]
Correct Answer: E
Solution :
Let \[I=\int_{0}^{2a}{\frac{f(x)dx}{f(x)+f(2a-x)}}\] ? (i) \[\Rightarrow \]\[I=\int_{0}^{2a}{\frac{f(2a-x)}{f(x)+f(2a-x)}}dx\] ?. (ii) On adding Eqs. (i) and (ii), we get \[2I=\int_{0}^{2a}{\frac{f(x)+f(2a-x)}{f(x)+f(2a-x)}}dx\] \[=\int_{0}^{2a}{1\,}dx=2a\] \[\Rightarrow \] \[I=a\]
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