Prove Proposition 12.1. Apply Lemma 12.1 and Fubini's theorem. If f(x, y) is continuous over the region

Prove Proposition 12.1. Apply Lemma 12.1 and Fubini's theorem.

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If f(x, y) is continuous over the region R defined by axband, c y d, then ba db ff f(x,y)dA = ff f(x, y)dx = f(x,y)dxdy R a This means that a double integral can be evaluated by iterated integrals and the order of integration can be changed. Note: If a, b, c, or d are functions, switching the order of integration will require rewriting the functions in term of xory based upon the order of integration.