Explanation The integral function is ∫ 0 4 ∫ − 4 − y ( y − 4 ) 2 d x d y . Calculation: Sketch the region for the integration as shown in Figure 1. Refer to Figure 1. Provide the reversed integration equivalent to the given integral as shown below. ∫ 0 4 ∫ − 4 − y ( y − 4 ) 2 d x d y = ∫ − 2 0 ∫ 2 x + 4 4 − x 2 d y d x Hence, the reversed integration equivalent to the given integral is ∫ − 2 0 ∫ 2 x + 4 4 − x 2 d y d x _ . Evaluate the integral ∫ − 2 0 ∫ 2 x + 4 4 − x 2 d y d x as shown below. ∫ − 2 0 ∫ 2 x + 4 4 − x 2 d y d x = ∫ − 2 0 ( y ) 2 x + 4 4 − x 2 d x = ∫ − 2 0 ( 4 − x 2 − ( 2 x + 4 ) ) d x = ∫ − 2 0 ( − x 2 − 2 x ) d x = ( − x 3 3 − 2 x 2 2 ) − 2 0 = ( 0 − ( − ( − 2 ) 3 3 − ( − 2 ) 2 ) ) = 0 − ( 8 3 − 4 ) = 4 3 Hence, the value of the reversed integral is 4 3 _

University Calculus: Early Transcendentals (4th Edition)

4th Edition

ISBN: 9780134995540

Author: Joel R. Hass, Christopher E. Heil, Przemyslaw Bogacki, Maurice D. Weir, George B. Thomas Jr.

Publisher: PEARSON

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Chapter 14, Problem 5PE

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Provide the sketch of the region of integration, provide the equivalent integral with the order of reversed integration, and calculate the value of the integrals.

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Chapter 14, Problem 4PE

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Chapter 14 Solutions

University Calculus: Early Transcendentals (4th Edition)

Ch. 14.1 - In Exercises 1-14. evaluate the iterated...Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - In Exercises 1-14, evaluate the iterated...Ch. 14.1 - In Exercises 1-14, evaluate the iterated...Ch. 14.1 - In Exercises 1-14, evaluate the iterated...Ch. 14.1 - In Exercises 1-14, evaluate the iterated integral....Ch. 14.1 - In Exercises 1-14, evaluate the iterated...Ch. 14.1 - In Exercises 1-14, evaluate the iterated integral....Ch. 14.1 - Prob. 10E

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Provide the sketch of the region of integration , provide the equivalent integral with the order of reversed integration, and calculate the value of the integrals.

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Provide the sketch of the region of integration, provide the equivalent integral with the order of reversed integration, and calculate the value of the integrals.

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Chapter 14 Solutions