Explanation Given: The double integral ∫ ∫ R x ln y d A , where R = [ 0 , 3 ] × [ 1 , e ] R denotes the points such that 0 ≤ x ≤ 3 , 1 ≤ y ≤ e Formula used: The integral formula ∫ x d x = x 2 2 and ∫ ln x d x = x ln x − x Calculation: To compute the double integral ∫ ∫ R x ln y d A , R = [ 0 , 3 ] × [ 1 , e ] first evaluate the inner integral treating ‘ y’ as constant with respect to ‘ x’ where x varies from ‘0’ to ‘3’ S ( y ) = ∫ 0 3 x ln y d x = ln <

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ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Chapter 15.1, Problem 43E

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Evaluate the integral ∫∫RxlnydA, where R=[0,3]×[1,e]

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Chapter 15.1, Problem 42E

Chapter 15.1, Problem 44E

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Chapter 15 Solutions

Calculus: Early Transcendentals

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Evaluate the integral ∫ ∫ R x ln y d A , where R = [ 0 , 3 ] × [ 1 , e ]

Solution Summary: The author explains how to compute the double integral, based on the formula displaystyle

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Evaluate the integral ∫∫RxlnydA, where R=[0,3]×[1,e]

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Chapter 15 Solutions