Question: Let H be a closed, connected, nonempty Jordan region and suppose that f: H R is continuous. If g: H R is integrable and nonnegative

Let H be a closed, connected, nonempty Jordan region and suppose that f: H †’ R is continuous. If g: H †’ R is integrable and nonnegative on H, prove that there is an x0 ˆˆ H such that

f(x0) g(x) dx = f(x)g(x) dx.

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