Explanation For finding the flux across the net, we have to find the surface integral by parameterizing and then we can evaluate it. Given: The force function and the points are given below. v = ( x − y , z + y + 4 , z 2 ) a n d y=1-x 2 − z 2 , y ≥ 0. Formula Used: ∬ s v . d s = ∬ R v ( G ( r , θ ) . N ( r , θ ) d r d θ Calculation: Let x = r cos ( θ ) , z = r sin ( θ ) ,then y=1-r 2 with 0 ≤ θ ≤ 2 π ,0 ≤ r ≤ 1 Now G ( r , θ ) = ( r cos ( θ ) , 1 − r 2 , r sin ( θ ) ) T r ( r , θ ) = ( cos ( θ ) , − 2 r , sin ( θ ) ) T θ ( r , θ ) = ( − r s i n ( θ ) , 0 , r c o s ( θ ) ) Then, the normal vector is N ( r , θ ) = T r ( r , θ ) x T θ ( r , θ ) = | i j k cos θ − 2 r sin θ − r sin θ 0 r cos θ | = i ( − 2 r 2 cos θ ) − j ( r ) + k ( − 2 r 2 sin θ ) = ( − 2 r 2 cos

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 17.5, Problem 26E

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To calculate: The flux across the net in the river.

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Chapter 17.5, Problem 25E

Chapter 17.5, Problem 27E

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Chapter 17 Solutions

CALCULUS (CLOTH)

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The flux across the net in the river.

Solution Summary: The author calculates the flux across the net in the river by finding the surface integral by parameterizing and then evaluating it.

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To calculate: The flux across the net in the river.

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Chapter 17 Solutions