If f (a + b - x) = f (x) , then _a^b ,x.f ,(a + b - x) ,dx = - Vidyadip

MCQ

If $f (a + b - x)$ $= f (x)$ , then $\int\limits_a^b {\,x.f\,(a + b - x)\,dx} $ $=$

A
$0$
B
$\frac{1}{2}$
✓
$\frac{{a + b}}{2}\int\limits_a^b {\,{\rm{f}}(x)\,dx} $
D
$\frac{{a - b}}{2}\int\limits_a^b {\,{\rm{f}}\,(x)\,dx} $

✓

Answer

Correct option: C.

$\frac{{a + b}}{2}\int\limits_a^b {\,{\rm{f}}(x)\,dx} $

c

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