Explanation To evaluate a line integral, it is necessary to express the curve C in terms of parametric equations and then integrate to get the value. Given: Curve is given by, F ( x , y ) = ( 3 z y − 1 , 4 x , − y ) , r ( t ) = ( e t , e t , t ) for − 1 ≤ t ≤ 1 Formula used: ∫ e x d x = e x Calculation: The parametric equations for the given points is x = y = e t and z = t. ∴ F → ⋅ d r → = ( 3 z y e t + 4 x e t − y ) d t ∴ F → ⋅ d r → = ( 3 t + 4 e 2 t − e t ) d t ∫ C F →

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 17.2, Problem 23E

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To determine: To calculate $\int_{C} \vec{F} \cdot d \vec{r}$ .

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Chapter 17.2, Problem 22E

Chapter 17.2, Problem 24E

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Chapter 17 Solutions

Calculus - Standalone book

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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To calculate ∫ C F → ⋅ d r → .

Solution Summary: The author explains that to evaluate a line integral, it is necessary to express the curve C in terms of parametric equations and then integrate to get the value.

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To determine: To calculate $\int_{C} \vec{F} \cdot d \vec{r}$ .

Want to see the full answer?

Chapter 17 Solutions

To calculate ∫ C F → ⋅ d r → .

Solution Summary: The author explains that to evaluate a line integral, it is necessary to express the curve C in terms of parametric equations and then integrate to get the value.

Concept explainers

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To determine: To calculate ∫CF→⋅dr→.

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Chapter 17 Solutions

To determine: To calculate $\int_{C} \vec{F} \cdot d \vec{r}$ .