definite-integral

Question: If $f(a+b-x)=f(x),$ then $\int_{a}^{b}{x\,f(x)\,dx=}$



1) $\frac{a+b}{2}\int_{a}^{b}{f(b-x)\,dx}$
2) $\frac{a+b}{2}\int_{a}^{b}{f(x)\,dx}$
3) $\frac{b-a}{2}\int_{a}^{b}{f(x)\,dx}$
4) None of these
Solution: Explanation: No Explanation
Properties of definite integration

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