Explanation Given : A solid with A as the area of the front face of the solid. Proof : Step 1: Let us denote M as the length of the other side of the rectangle which forms the base of the solid. The volume of the solid is the double integral of the function f(x,y) =g(x) over the rectangle R = [ 0 , M ] × [ 0 , L ] V = ∫ ∫ R g ( x ) d A Step 2: We use Fubini's Theorem to define the double integral as iterated integral and then when we compute the resulting integral as the product of two single integrals, we get V = ∫ ∫ R g ( x ) d A = V = ∫ 0 L ∫ 0 M g ( x )

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 16.1, Problem 51E

To determine

To prove: Using Fubini's Theorem, the mathematical proof of the statement stating that the solid shown in figure has volume AL, where A is the area of the front face of the solid.

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Chapter 16.1, Problem 50E

Chapter 16.1, Problem 52E

Chapter 16 Solutions

CALCULUS (CLOTH)

Ch. 16.1 - Prob. 1PQ Ch. 16.1 - Prob. 2PQ Ch. 16.1 - Prob. 3PQ Ch. 16.1 - Prob. 4PQ Ch. 16.1 - Prob. 5PQ Ch. 16.1 - Prob. 6PQ Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E

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Prob. 2E Ch. 16.5 - Prob. 3E Ch. 16.5 - Prob. 4E Ch. 16.5 - Prob. 5E Ch. 16.5 - Prob. 6E Ch. 16.5 - Prob. 7E Ch. 16.5 - Prob. 8E Ch. 16.5 - Prob. 9E Ch. 16.5 - Prob. 10E Ch. 16.5 - Prob. 11E Ch. 16.5 - Prob. 12E Ch. 16.5 - Prob. 13E Ch. 16.5 - Prob. 14E Ch. 16.5 - Prob. 15E Ch. 16.5 - Prob. 16E Ch. 16.5 - Prob. 17E Ch. 16.5 - Prob. 18E Ch. 16.5 - Prob. 19E Ch. 16.5 - Prob. 20E Ch. 16.5 - Prob. 21E Ch. 16.5 - Prob. 22E Ch. 16.5 - Prob. 23E Ch. 16.5 - Prob. 24E Ch. 16.5 - Prob. 25E Ch. 16.5 - Prob. 26E Ch. 16.5 - Prob. 27E Ch. 16.5 - Prob. 28E Ch. 16.5 - Prob. 29E Ch. 16.5 - Prob. 30E Ch. 16.5 - Prob. 31E Ch. 16.5 - Prob. 32E Ch. 16.5 - Prob. 33E Ch. 16.5 - Prob. 34E Ch. 16.5 - Prob. 35E Ch. 16.5 - Prob. 36E Ch. 16.5 - Prob. 37E Ch. 16.5 - Prob. 38E Ch. 16.5 - Prob. 39E Ch. 16.5 - Prob. 40E Ch. 16.5 - Prob. 41E Ch. 16.5 - Prob. 42E Ch. 16.5 - Prob. 43E Ch. 16.5 - Prob. 44E Ch. 16.5 - Prob. 45E Ch. 16.5 - Prob. 46E Ch. 16.5 - Prob. 47E Ch. 16.5 - Prob. 48E Ch. 16.5 - Prob. 49E Ch. 16.5 - 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To prove : Using Fubini's Theorem, the mathematical proof of the statement stating that the solid shown in figure has volume AL, where A is the area of the front face of the solid.

Solution Summary: The author explains how Fubini's Theorem proves that the solid shown in figure has volume AL, where A is the area of the front face

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To prove: Using Fubini's Theorem, the mathematical proof of the statement stating that the solid shown in figure has volume AL, where A is the area of the front face of the solid.

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Chapter 16 Solutions