If \[f(a+b-x)=f(x),\] then \[\int_{a}^{b}{x\,f(x)\,dx=}\] [CEE 1993; AIEEE 2003]

\[\frac{b-a}{2}\int_{a}^{b}{f(x)\,dx}\]

\[\frac{a+b}{2}\int_{a}^{b}{f(b-x)\,dx}\]

\[\frac{a+b}{2}\int_{a}^{b}{f(x)\,dx}\]

If \[f(a+b-x)=f(x),\] then \[\int_{a}^{b}{x\,f(x)\,dx=}\] [CEE 1993; A

1.	If \[f(a+b-x)=f(x),\] then \[\int_{a}^{b}{x\,f(x)\,dx=}\] [CEE 1993; AIEEE 2003]
A.	\[\frac{a+b}{2}\int_{a}^{b}{f(b-x)\,dx}\]
B.	\[\frac{a+b}{2}\int_{a}^{b}{f(x)\,dx}\]
C.	\[\frac{b-a}{2}\int_{a}^{b}{f(x)\,dx}\]
D.	None of these
Answer» C. \[\frac{b-a}{2}\int_{a}^{b}{f(x)\,dx}\]

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