Q101 / 170 · Manipal (MET) 2017 · Mathematics

$\int_0^{2 a} \frac{f(x)}{f(x)+f(2 a-x)} d x$ is equal to

  • Correct answer
    A
    a
  • B
    -a
  • C
    1
  • D
    0

Solution

Let $I=\int_0^{2 a} \frac{f(x)}{f(x)+f(2 a-x)} d x...(i)$ $I=\int_0^{2 a} \frac{f(2 a-x)}{f(2 a-x)+f(x)} d x...(ii)$ On adding Eqs. (i) and (ii), we get $\begin{aligned} 2 I & =\int_0^{2 a} \frac{f(2 a-x)+f(x)}{f(2 a-x)+f(x)} d x=\int_0^{2 a} d x=2 a \\ \Rightarrow I & =a \end{aligned}$

Hence, the correct answer is option: 'A'.

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