Question

${\int }_0^{2t}\frac{f\left(x\right)}{f\left(x\right)+f(2t-x)}dx$

• A. 2t
• B. 3t
• C. t
• D. t/2

Answer 1

Answer: (C)

t

Let $I={\int }_0^{2t}\frac{f\left(x\right)}{f\left(x\right)+f(2t-x)}dx$ ...(1)
Using integration property
$I={\int }_0^{2t}\frac{f(2t-x)}{f(2t-x)+f\left(x\right)}dx$ ...(2)
Adding (1) and (2), we get
$2I={\int }_0^{2t}dx=2t$

$\Rightarrow I=t$