A) \[0\]
B) \[\frac{\pi }{4}\]
C) \[a\]
D) none of these
Correct Answer: C
Solution :
\[I=\int_{0}^{2a}{\frac{f(x)}{f(x)+f(2a-x)}dx}\] ? (i) \[\Rightarrow I=\int_{0}^{2a}{\frac{f(2a-x)}{f(2a-x)+f(x)}dx}\] ? (ii) Adding (1) and (2). \[2I=\int_{0}^{2a}{\frac{f(x)+f(2a-x)}{f(x)+f(2a-x)}dx=[x]_{0}^{2a}}\] \[\Rightarrow \]\[I=a\]
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