Explanation For funding thesurface integral across the given surface,we have to find the surface integral by parameterizing and then evaluate it. Given: The force function and the points are given below. F = ( x z , y z , z − 1 ) x 2 + y 2 = 9 , z = 4. Formula used: ∬ s F . d S = ∬ R F ( G ( r , θ ) . N ( r , θ ) d r d θ Calculation: let By parameterizing x = r cos θ , y = r sin θ , z = 4 w i t h R = { ( x , y ) | 0 ≤ r ≤ 3 , 0 ≤ θ ≤ 2 π } . G ( r , θ ) = ( r cos θ , r sin θ , 4 ) Now G ( r , θ ) = ( r cos θ , r sin θ , 4 ) then T r ( r , θ ) = ( c o s θ , s i n θ , 0 ) T θ ( r , θ ) = ( − r s i n θ , r c o s θ , 0 ) Then normal vector is N ( r , θ ) = T r ( r , θ ) x T θ ( ...

4th Edition

ISBN: 9781319308858

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 16.5, Problem 13E

To determine

To calculate: The surface integral for given vector function and surface.

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Chapter 16.5, Problem 12E

Chapter 16.5, Problem 14E

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Chapter 16 Solutions

CALCULUS:EARLY TRANS.(LL)-W/ACCESS

Ch. 16.1 - Prob. 1PQ Ch. 16.1 - Prob. 2PQ Ch. 16.1 - Prob. 3PQ Ch. 16.1 - Prob. 4PQ Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E Ch. 16.1 - Prob. 5E Ch. 16.1 - Prob. 6E

Ch. 16.1 - Prob. 7E Ch. 16.1 - Prob. 8E Ch. 16.1 - Prob. 9E Ch. 16.1 - Prob. 10E Ch. 16.1 - Prob. 11E Ch. 16.1 - Prob. 12E Ch. 16.1 - Prob. 13E Ch. 16.1 - Prob. 14E Ch. 16.1 - Prob. 15E Ch. 16.1 - Prob. 16E Ch. 16.1 - Prob. 17E Ch. 16.1 - Prob. 18E Ch. 16.1 - Prob. 19E Ch. 16.1 - Prob. 20E Ch. 16.1 - Prob. 21E Ch. 16.1 - Prob. 22E Ch. 16.1 - Prob. 23E Ch. 16.1 - Prob. 24E Ch. 16.1 - Prob. 25E Ch. 16.1 - Prob. 26E Ch. 16.1 - Prob. 27E Ch. 16.1 - Prob. 28E Ch. 16.1 - Prob. 29E Ch. 16.1 - Prob. 30E Ch. 16.1 - Prob. 31E Ch. 16.1 - Prob. 32E Ch. 16.1 - Prob. 33E Ch. 16.1 - Prob. 34E Ch. 16.1 - Prob. 35E Ch. 16.1 - Prob. 36E Ch. 16.1 - Prob. 37E Ch. 16.1 - Prob. 38E Ch. 16.1 - Prob. 39E Ch. 16.1 - Prob. 40E Ch. 16.1 - Prob. 41E Ch. 16.1 - Prob. 42E Ch. 16.1 - Prob. 43E Ch. 16.1 - Prob. 44E Ch. 16.1 - Prob. 45E Ch. 16.1 - Prob. 46E Ch. 16.1 - Prob. 47E Ch. 16.1 - Prob. 48E Ch. 16.1 - Prob. 49E Ch. 16.1 - Prob. 50E Ch. 16.1 - Prob. 51E Ch. 16.1 - Prob. 52E Ch. 16.1 - Prob. 53E Ch. 16.1 - Prob. 54E Ch. 16.1 - 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