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 F → = 2 y 2 j ^ and the tetrahedron bounded by the coordinate planes and the plane D : x + 4 y + z = 8 . Here, ∬ S F → ⋅ N → d s = ∬ D 〈 0 , 2 y 2 , 0 〉 ⋅ 〈 − ( − x 8 − x − 4 y ) , − ( − y 8 − x − 4 y ) , 1 〉 d A = ∬ D [ 2 y 3 8 − x − 4 y ] d A = ∫ 0 2 π Ȣ

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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Question

Chapter 13.7, Problem 9PS

To determine

To verify: The divergence theorem for the vector function F→=2y2j^ and the tetrahedron bounded by the coordinate planes and the plane D:x+4y+z=8 .

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Chapter 13.7, Problem 8PS

Chapter 13.7, Problem 10PS

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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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To verify: The divergence theorem for the vector function F → = 2 y 2 j ^ and the tetrahedron bounded by the coordinate planes and the plane D : x + 4 y + z = 8 .

Solution Summary: The author explains the divergence theorem for the vector function stackrelto, which states that, Let S be a smooth, orientable surface that encloses

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To verify: The divergence theorem for the vector function F→=2y2j^ and the tetrahedron bounded by the coordinate planes and the plane D:x+4y+z=8 .

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Chapter 13 Solutions