JEE Main & Advanced Sample Paper JEE Main Sample Paper-38

  • question_answer 84) Value of\[\int_{0}^{2a}{\frac{f(x)}{f(x)+f(2a-x)}dx}\]is

    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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