Explanation Given: The function f is continuous, such that 0 ≤ f ( x , y ) ≤ 1 over a region R of area 1 unit. Proof: The function f is continuous, such that: 0 ≤ f ( x , y ) ≤ 1 Take the double integral over this inequality on the region R , which gives: ∬ R ( 0 ) d A ≤ ∬ R f ( x , y ) d A ≤ ∬ R ( 1 ) d A 0

11th Edition

ISBN: 9781337275378

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Chapter 14.2, Problem 65E

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To prove: The inequality of the function as 0≤∬Rf(x,y)dA≤1.

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Chapter 14.2, Problem 64E

Chapter 14.2, Problem 66E

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To prove: The inequality of the function as 0 ≤ ∬ R f ( x , y ) d A ≤ 1 .

Solution Summary: The author explains the inequality of the function f, which is continuous over a region R of area 1 unit.

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To prove: The inequality of the function as 0≤∬Rf(x,y)dA≤1.

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Chapter 14 Solutions