Explanation According to Fubini’s theorem, if f ( x , y , z ) is defined and is continuous on B , then the triple integral of ∭ B f d v is expressed as any one of the six iterated integrals ∭ B f d v = ∫ a b ∫ e d ∫ r s f ( x , y , z ) d z d y d x Proof: Let B = [ a , b ] × [ c , d ] × [ r , s ] and ‖ P ‖ denotes the length of the longest diagonal in P hence we get: B = [ a , b ] × [ c , d ] × [ r , s ] P = P 1 × P 2 × P 3 Let V = volume of B and let ( x k * , y k * , z k * ) ∈ V k Hence let Δ V k = volume of V k , now

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 12, Problem 11PE

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To state: Fubini’s theorem over a parallelepiped in space.

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Chapter 12, Problem 10PE

Chapter 12, Problem 12PE

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Chapter 12 Solutions

Calculus

Ch. 12.1 - Prob. 1PS Ch. 12.1 - Prob. 2PS Ch. 12.1 - Prob. 3PS Ch. 12.1 - Prob. 4PS Ch. 12.1 - Prob. 5PS Ch. 12.1 - Prob. 6PS Ch. 12.1 - Prob. 7PS Ch. 12.1 - Prob. 8PS Ch. 12.1 - Prob. 9PS Ch. 12.1 - Prob. 10PS

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