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 → = x 2 i ^ + y 2 j ^ + z 2 k ^ and the sphere S : x 2 + y 2 + z 2 = 4 . The value of the integral ∬ S F → ⋅ N → d s can be evaluated as, ∬ S F → ⋅ N → d</

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ISBN: 9781465208880

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

Publisher: Kendall Hunt Publishing

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Chapter 13.7, Problem 33PS

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To calculate: The value of the surface integral ∬SF→⋅N→ds for F→=x2i^+y2j^+z2k^ and the sphere S:x2+y2+z2=4 .

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Chapter 13.7, Problem 32PS

Chapter 13.7, Problem 34PS

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The value of the surface integral ∬ S F → ⋅ N → d s for F → = x 2 i ^ + y 2 j ^ + z 2 k ^ and the sphere S : x 2 + y 2 + z 2 = 4 .

Solution Summary: The author calculates the value of the surface integral displaystyleundersetSiint

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To calculate: The value of the surface integral ∬SF→⋅N→ds for F→=x2i^+y2j^+z2k^ and the sphere S:x2+y2+z2=4 .

Want to see the full answer?

Chapter 13 Solutions