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 → = curl [ ( e x z ) i ^ − 4 j ^ + ( sin x y z ) k ^ ] and the ellipsoid S : 2 x 2 + 3 y 2 + 7 z 2 = 1

6th Edition

ISBN: 9781465208880

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

Publisher: Kendall Hunt Publishing

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Chapter 13.7, Problem 28PS

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To calculate: The value of the surface integral ∬SF→⋅N→ds for F→=curl[(exz)i^−4j^+(sinxyz)k^] and the ellipsoid S:2x2+3y2+7z2=1 .

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Chapter 13.7, Problem 27PS

Chapter 13.7, Problem 29PS

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The value of the surface integral ∬ S F → ⋅ N → d s for F → = curl [ ( e x z ) i ^ − 4 j ^ + ( sin x y z ) k ^ ] and the ellipsoid S : 2 x 2 + 3 y 2 + 7 z 2 = 1 .

Solution Summary: The author explains the divergence theorem, where the value of the surface integral is 0.

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To calculate: The value of the surface integral ∬SF→⋅N→ds for F→=curl[(exz)i^−4j^+(sinxyz)k^] and the ellipsoid S:2x2+3y2+7z2=1 .

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Chapter 13 Solutions