If , then is equal…

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

40. If f(a+b−x)=f(x)f(a+b-x)=f(x), then ∫abxf(x)dx\int_{a}^{b} x f(x) d x is equal to (A) a+b2∫abf(b−x)dx\frac{a+b}{2} \int_{a}^{b} f(b-x) d x (B) a+b2∫abf(b+x)dx\frac{a+b}{2} \int_{a}^{b} f(b+x) d x (C) b−a2∫abf(x)dx\frac{b-a}{2} \int_{a}^{b} f(x) d x (D) a+b2∫abf(x)dx\frac{a+b}{2} \int_{a}^{b} f(x) d x

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