Suppose (x, y) is continuous over a region R in the plane and that the area A(R)

Suppose ƒ(x, y) is continuous over a region R in the plane and that the area A(R) of the region is defined. If there are constants m and M such that m ≤ ƒ(x, y) ≤ M for all (x, y)ε R, prove that

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mA(R) < ffs f(x, y) dAMA(R). R