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 → = x i ^ + y j ^ + ( z 2 − 1 ) k ^ and the surface of a solid bounded by the cylinder S : x 2 + y 2 = 4 and the planes z = 0 and z = 1

7th Edition

ISBN: 9781524916817

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

Publisher: Kendall Hunt Publishing

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Chapter 13.7, Problem 35PS

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To calculate: The value of the surface integral ∬SF→⋅N→ds for F→=xi^+yj^+(z2−1)k^ and the surface of a solid bounded by the cylinder S:x2+y2=4 and the planes z=0 and z=1 .

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Chapter 13.7, Problem 34PS

Chapter 13.7, Problem 36PS

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Chapter 13 Solutions

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The value of the surface integral ∬ S F → ⋅ N → d s for F → = x i ^ + y j ^ + ( z 2 − 1 ) k ^ and the surface of a solid bounded by the cylinder S : x 2 + y 2 = 4 and the planes z = 0 and z = 1 .

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

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To calculate: The value of the surface integral ∬SF→⋅N→ds for F→=xi^+yj^+(z2−1)k^ and the surface of a solid bounded by the cylinder S:x2+y2=4 and the planes z=0 and z=1 .

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Chapter 13 Solutions