Definite Integration Question 107
Question: $ \int_0^{2a}{\frac{f(x)}{f(x)+f(2a-x)}dx=} $
[IIT 1988; Karnataka CET 2000]
Options:
A) $ a $
B) $ \frac{a}{2} $
C) $ 2a $
D) 0
Show Answer
Answer:
Correct Answer: A
Solution:
$ I=\int_0^{2a}{\frac{f(x)}{f(x)+f(2a-x)}dx} $ ……(i)
$ I=\int_0^{2a}{\frac{f(2a-x)}{f(2a-x)+f(x)}}dx $ ……(ii)
Adding (i) and (ii), we get $ 2I=\int_0^{2a}{dx=2a\Rightarrow I=a} $ .
BETA
