_0^ 2a f(x) f(x) + f(2a - x) ,dx = - Vidyadip

MCQ

$\int_0^{2a} {\frac{{f(x)}}{{f(x) + f(2a - x)}}\,dx = } $

✓
$a$
B
$\frac{a}{2}$
C
$2a$
D
$0$

✓

Answer

Correct option: A.

$a$

a
(a) $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} $.

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