Explanation Concept used: The divergence theorem states that, Let S be a smooth, orientable surface that encloses a solid region R in ℝ 3 . If F → is a continuous vector field whose components have continuous partial derivatives in an open set containing R , then ∬ S F → ⋅ N → d s = ∭ R div F → d V ; where N → is the outward unit normal field for the surface S . Consider the vector function ∬ S F → ⋅ N → d s for F → = 2 y i ^ − z j ^ + 3 x k ^ and the unit cube S : 0 ≤ x ≤ 1 , 0 ≤ y ≤ 1 , 0 ≤ z ≤ 1

Student's Solution and Survival Manual for Calculus

7th Edition

ISBN: 9781524934040

Author: STRAUSS MONTY J, TODA MAGDALENA DANIELE, SMITH KARL J

Publisher: Kendall Hunt Publishing

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Chapter 13.7, Problem 30PS

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To calculate: The value of the surface integral ∬SF→⋅N→ds for F→=2yi^−zj^+3xk^ and the unit cube S:0≤x≤1,0≤y≤1,0≤z≤1 .

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Chapter 13.7, Problem 29PS

Chapter 13.7, Problem 31PS

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Chapter 13 Solutions

Student's Solution and Survival Manual for Calculus

Ch. 13.1 - Prob. 1PS Ch. 13.1 - Prob. 2PS Ch. 13.1 - Prob. 3PS Ch. 13.1 - Prob. 4PS Ch. 13.1 - Prob. 5PS Ch. 13.1 - Prob. 6PS Ch. 13.1 - Prob. 7PS Ch. 13.1 - Prob. 8PS Ch. 13.1 - Prob. 9PS Ch. 13.1 - Prob. 10PS

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The value of the surface integral ∬ S F → ⋅ N → d s for F → = 2 y i ^ − z j ^ + 3 x k ^ and the unit cube S : 0 ≤ x ≤ 1 , 0 ≤ y ≤ 1 , 0 ≤ z ≤ 1 .

Solution Summary: The author explains the divergence theorem, where S is a smooth, orientable surface whose components have continuous partial derivatives in R.

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To calculate: The value of the surface integral ∬SF→⋅N→ds for F→=2yi^−zj^+3xk^ and the unit cube S:0≤x≤1,0≤y≤1,0≤z≤1 .

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Chapter 13 Solutions