The correct option is A a Let I= #160; ∫_0^2af(x)f(x)+f(2a x)dx ......(1).or, I= #160; ∫_0^2af(2a x)f(2a x)+f(x)dx [ Using proper ...

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Property 1

∫02afxfx+f2a-...

Question

$2 a \int 0 \frac{f (x)}{f (x) + f (2 a - x)} d x =$

a

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2 a

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0

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none of these

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Solution

The correct option is A $a$
Let $I =$ $2 a \int 0 \frac{f (x)}{f (x) + f (2 a - x)} d x$ ......(1).
or, $I =$ $2 a \int 0 \frac{f (2 a - x)}{f (2 a - x) + f (x)} d x$ [ Using property of definite integral]......(2).
Now, adding (1) and (2) we get,
$2 I =$ $2 a \int 0 d x$
or, $2 I = 2 a$
or, $I = a$ .

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