Explanation Given information: The given line integral is ∫ C y d x + z d y + x d z . Formula used: Suppose that curve C is defined by the vector function r = r ( t ) where a ≤ t ≤ b , then the line integral of ∫ C P ( y ) d x + Q ( z ) d y + R ( x ) d z is given by ∫ a b ( P ( r ( t ) ) d x d t + Q ( r ( t ) ) d y d t + R ( r ( t ) ) d z d t ) d t Calculation: Consider the given curve. C : r ( t ) = 〈 2 + t − 1 , t 3 , t 2 〉 , 0 ≤ t ≤ 1 Parameterized the curve by considering the following. x = 2 + t − 1 , y = t 3 , z = t 2 , 0 ≤ t ≤ 1 So, d y = 3 t 2 d t d x = − 1 t 2 d z = 2 t d t The value of the line integral can be calculated as shown below

4th Edition

ISBN: 9781319055905

Author: FRANZOSA

Publisher: VST

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Question

Chapter 16.2, Problem 30E

To determine

To evaluate:

The given line integral over the curve r(t)=〈2+t−1,t3,t2〉 and 0≤t≤1.

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Chapter 16.2, Problem 29E

Chapter 16.2, Problem 31E

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Chapter 16 Solutions

EBK CALCULUS: EARLY TRANSCENDENTALS

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Knowledge Booster

The given line integral over the curve r ( t ) = 〈 2 + t − 1 , t 3 , t 2 〉 and 0 ≤ t ≤ 1 .

Solution Summary: The author evaluates the given line integral over the curve by considering the following.

To evaluate:

The given line integral over the curve r(t)=〈2+t−1,t3,t2〉 and 0≤t≤1.

Want to see the full answer?

Chapter 16 Solutions

The given line integral over the curve r ( t ) = 〈 2 + t − 1 , t 3 , t 2 〉 and 0 ≤ t ≤ 1 .

Solution Summary: The author evaluates the given line integral over the curve by considering the following.

To evaluate: The given line integral over the curve r(t)=〈2+t−1,t3,t2〉 and 0≤t≤1.

Want to see the full answer?

Chapter 16 Solutions

To evaluate:

The given line integral over the curve r(t)=〈2+t−1,t3,t2〉 and 0≤t≤1.