The Mean Value Theorem for double integrals says that if f is a continuous function on a plane region D that is of type I or II, then there exists a point (x 0 , y 0 ) in D such that Use the Extreme Value Theorem (14 7 8) and Property 15 2 11 of integrals to prove this theorem (Use the proof of the single variable version in Section 6 5 as a guide ) f(x, y) dA f(xo, Yo) A(D)

Question: The Mean Value Theorem for double integrals says that if f is a continuous function on a plane region D that is of type I

The Mean Value Theorem for double integrals says that if f is a continuous function on a plane region D that is of type I or II, then there exists a point (x₀, y₀) in D such that

| f(x, y) dA = f(xo, Yo) A(D)

Use the Extreme Value Theorem (14.7.8) and Property 15.2.11 of integrals to prove this theorem. (Use the proof of the single-variable version in Section 6.5 as a guide.)

| f(x, y) dA = f(xo, Yo) A(D)

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