Explanation The double integral is ∫ − 2 2 ∫ 1 2 ∫ 1 e x y 2 z d z d x d y . In order to obtain the double integral, integrate the innermost integral first. ∫ 1 e x y 2 z d z = x y 2 [ ln z ] 1 e = x y 2 [ ln e + ln 1 ] = x y 2 Now, obtain the middle integral with the help of the result of innermost integral as follows. ∫ 1 2 ( x y 2 ) d x = y 2 [ x 2 2 ] 1 2 = y 2 [ ( 2 ) 2 2 − ( 1 ) 2 2 ] = y 2 [ 2 − 1 2 ] = 3 2 y 2 Now, obtain the outer integral with the help of the result of innermost integral as follows

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 29.4, Problem 28E

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Chapter 29.4, Problem 27E

Chapter 29.4, Problem 29E

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Chapter 29 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

Ch. 29.1 - Practice Exercise If f(x, y) = 4xy2 – 3x2y, find...Ch. 29.1 - Prob. 1E Ch. 29.1 - Prob. 2E Ch. 29.1 - Prob. 3E Ch. 29.1 - Prob. 4E Ch. 29.1 - Prob. 5E Ch. 29.1 - Prob. 6E Ch. 29.1 - Prob. 7E Ch. 29.1 - Prob. 8E Ch. 29.1 - Prob. 9E

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The volume with the help of double integration .

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Chapter 29 Solutions