Explanation Given information: The given integral is ∫ C y d x + z d y + x d z over r ( t ) = ( 2 + t − 1 , t 3 , t 2 ) for 0 ≤ t ≤ 1 . Concept Used: The line integral over the curve C is given by ∫ C P d x + Q d y + R d z = ∫ a b [ P ( x ( t ) , y ( t ) , z ( t ) ) d x d t + Q ( x ( t ) , y ( t ) , z ( t ) ) d y d t + R ( x ( t ) , y ( t ) , z ( t ) ) d z d t ] d t where r ( t ) = ( x ( t ) , y ( t ) , z ( t ) ) is the parametrization of the given curve C. Calculation: As given ∫ C y d x + z d y + x d z with r ( t ) = ( 2 + t − 1 , t 3 , t 2 ) for 0 ≤ t ≤ 1 , thus ∫ C f ⋅ d r = ∫ a b [ P ( x ( t ) , y ( t ) , z ( t ) ) d x d t + Q ( x ( t ) , y

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 17.2, Problem 30E

To determine

To find: The line integral ∫Cydx+zdy+xdz over r(t)=(2+t−1,t3,t2) for 0≤t≤1 .

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Chapter 17.2, Problem 29E

Chapter 17.2, Problem 31E

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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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The line integral ∫ C y d x + z d y + x d z over r ( t ) = ( 2 + t − 1 , t 3 , t 2 ) for 0 ≤ t ≤ 1 .

Solution Summary: The author explains that 4110 is the line integral over the curve C.

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To find: The line integral ∫Cydx+zdy+xdz over r(t)=(2+t−1,t3,t2) for 0≤t≤1 .

Want to see the full answer?

Chapter 17 Solutions