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 ) , 0 , r sin ( θ ) ) T r ( r , θ ) = ( cos ( θ ) , 0 , sin ( θ ) ) T θ ( r , θ ) = ( − r s i n ( θ ) , 0 , r c o s ( θ ) ) Then normal vector is, N ( r , θ ) = T r ( r , θ ) x T θ ( r , θ ) = | i j k cos θ 0 sin θ − r sin θ 0 r cos θ

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 17.5, Problem 25E

To determine

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

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Chapter 17.5, Problem 24E

Chapter 17.5, Problem 26E

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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 explains how to calculate the flux across the net in the river by finding the surface integral 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