Question

The value of integral ${\int }_0^{2a}\frac{f(x)}{f(x)+f(2a-x)}dx,$ where $f(x)$ is a continuous function, is

• A. 0
• B. 1
• C. $a$
• D. $2a$

Answer 1

Answer: (C)

Let $I={\int }_0^{2a}\frac{f(x)}{f(x)+f(2a-x)}dx$ ...(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
$2I={\int }_0^{2a}1dx\Rightarrow 2I[x{]}_0^{2a}$
$\Rightarrow$ $2I=2a$
$\Rightarrow$ $I=a$