Explanation Given: f ( x , y , z ) = ( z y + x y + x z ) and F ( x , y , z ) = ∇ f ( x , y , z ) . Calculation: ∇ f ( x , y , z ) = ( d d x f ( x , y , z ) , d d y f ( x , y , z ) , d d z f ( x , y , z ) ) ð ∇ f ( x , y , z ) = ( y + z , x + z , x + y ) . ð F ( x , y , z ) = ( y + z , x + z , x + y ) . For r 1 , r 1 = ( t , t , 1 ) and 0 ≤ t ≤ 1 ð ∫ c F . d r = ∫ c F . d r d t d t . ð d r d t = ( 1 , 1 , 1 ) . Now, we will find F ( x , y , z ) in terms of t. ð F ( x ( t ) , y ( t ) , z ( t ) ) = ( 2 t , 2 t , 2 t ) Then, we will plug all these values into the ∫ c F . d r d t d t . ð ∫ 0 1 ( 2 t , 2 t , 2 t ) . ( 1 , 1 , 1 ) d t ...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied unde…

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Chapter 17.3, Problem 22E

To determine

The value of $\int_{c} F . d r$

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Chapter 17.3, Problem 21E

Chapter 17.3, Problem 23E

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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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