Prove the following extension of the Fundamental Theorem of Calculus to two variables: If 2 F/x

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Prove the following extension of the Fundamental Theorem of Calculus to two variables: If ∂²F/∂x ∂y = ƒ(x, y), then

R f(x,y) dA= F(b,d) - F(a,d) - F(b,c) + F(a, c)

where R = [a, b] × [c, d].

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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Question Posted: Jan 17, 2024 03:03 AM

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Prove the following extension of the Fundamental Theorem of Calculus to two variables: If 2 F/x

Question:

R f(x,y) dA= F(b,d) - F(a,d) - F(b,c) + F(a, c)

Step by Step Answer:

By Fubinis Theorem we get THEOREM 3 Fubinis T...View the full answer

Calculus

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