Explanation Given information: A curve C is specified by C : r ( t ) = 〈 t 3 , 2 , t 2 〉 , 0 ≤ t ≤ 1 A vector valued function F ( x , y , z ) = 〈 1 y 3 + 1 , 1 z + 1 , 1 〉 Formula used: Suppose that curve Cis a parametric curve r ( t ) where a ≤ t ≤ b , then the line integral of ∫ C F ⋅ d r is given by ∫ C F ⋅ d r = ∫ C F ( r ( t ) ) ⋅ r ′ ( t ) d t Calculation: Consider the given curve. C : r ( t ) = 〈 t 3 , 2 , t 2 〉 and 0 ≤ t ≤ 1 So, r ′ ( t ) = 〈 3 t 2 , 0 , 2 t 〉 And F ( r ( t ) ) = F ( t 3 , 2 , t 2 ) = 〈 1 9 , 1 t 2 + 1 , 1 〉 The value of the line integral can be calculated as shown below

4th Edition

ISBN: 9781319055905

Author: FRANZOSA

Publisher: VST

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

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Question

Chapter 16.2, Problem 25E

To determine

To evaluate:

The integral ∫CF⋅dr for the oriented curve specified.

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Chapter 16.2, Problem 24E

Chapter 16.2, Problem 26E

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Chapter 16 Solutions

EBK CALCULUS: EARLY TRANSCENDENTALS

Ch. 16.1 - Prob. 1PQ Ch. 16.1 - Prob. 2PQ Ch. 16.1 - Prob. 3PQ Ch. 16.1 - Prob. 4PQ Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E Ch. 16.1 - Prob. 5E Ch. 16.1 - Prob. 6E

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