If and are continuous functions satisfying and

MATHEMATICS · Subjective · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

f

and

g

are continuous functions satisfying

f(x) = f(a-x)

and

g(x) + g(a-x) = 2

, then show that

\int_{0}^{a} f(x) g(x) dx = \int_{0}^{a} f(x) dx