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. v = ( y , z , x ) a n d 3 x - 4 y + z = 1 a n d 0 ≤ x ≤ 1 , 0 ≤ y ≤ 1. Formula Used: ∬ s F . d s = ∬ R F ( G ( x , z ) . N ( x , z ) d x d y Calculation: let x = x , y = y , t h e n z = 1 − 3 x + 4 y with 0 ≤ x ≤ 1 , 0 ≤ y ≤ 1 Now G ( x , z ) = ( x , y , 1 − 3 x + 4 y ) T x ( x , z ) = ( 1 , 0 , − 3 ) T z ( x , z ) = ( 0 , 1 , 4 ) Then normal vector is N ( x , z ) = T x ( x , z ) x T z ( x , z ) = | i j k 1 0 − 3 0 1 4 | = i ( 0 + 3 ) − j ( 4 ) + k ( 1 ) = ( 3 , − 4 , 1 ) sin c e 1 > 0 so the normal pointing out toward upward direction so we have to ta...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 17.5, Problem 5E

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

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Chapter 17.5, Problem 4E

Chapter 17.5, Problem 6E

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Chapter 17 Solutions

CALCULUS (CLOTH)

Ch. 17.1 - Prob. 1PQ Ch. 17.1 - Prob. 2PQ Ch. 17.1 - Prob. 3PQ Ch. 17.1 - Prob. 4PQ Ch. 17.1 - Prob. 1E Ch. 17.1 - Prob. 2E Ch. 17.1 - Prob. 3E Ch. 17.1 - Prob. 4E Ch. 17.1 - Prob. 5E Ch. 17.1 - Prob. 6E

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Thesurface integral for given vector function and surface.

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Chapter 17 Solutions