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 i ^ + y j ^ + z k ^ and the cylinder S : x 2 + y 2 = 1 , for 0 ≤ z ≤ 1 , with the two disk ends included. The value of the integral ∬ S F → ⋅ N → d s can be evaluated as, ∬ S <

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 23PS

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To calculate: The value of the surface integral ∬SF→⋅N→ds for F→=xi^+yj^+zk^ and the cylinder S:x2+y2=1 , for 0≤z≤1 , with the two disk ends included.

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Chapter 13.7, Problem 22PS

Chapter 13.7, Problem 24PS

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Chapter 13 Solutions

Calculus

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The value of the surface integral ∬ S F → ⋅ N → d s for F → = x i ^ + y j ^ + z k ^ and the cylinder S : x 2 + y 2 = 1 , for 0 ≤ z ≤ 1 , with the two disk ends included.

Solution Summary: The author calculates the value of the surface integral stackrelto and the cylinder S:x2+y2.

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To calculate: The value of the surface integral ∬SF→⋅N→ds for F→=xi^+yj^+zk^ and the cylinder S:x2+y2=1 , for 0≤z≤1 , with the two disk ends included.

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Chapter 13 Solutions