Explanation Given information: The given line integral is ∫ C ( x − y ) d x + ( y − z ) d y + z d z . Formula used: Suppose that curve C is the line joining two points ( x 0 , y 0 , z 0 ) and ( x 1 , y 1 , z 1 ) 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 And r ( t ) = ( 1 − t ) ( x 0 , y 0 , z 0 ) + t ( x 1 , y 1 , z 1 ) and 0 ≤ t ≤ 1 Calculation: Consider the given points ( 0 , 0 , 0 ) and ( 1 , 4 , 4 ) . Here, ( x 0 , y 0 , z 0 ) = ( 0 , 0 , 0 ) and ( x 1 , y 1 , z 1 ) = ( 1 , 4 , 4 ) C : r ( t ) = ( 1 − t ) ( 0 , 0 , 0 ) + t ( 1 , 4 , 4 ) and 0 ≤ t ≤ 1 Parameterized the curve by considering the following

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ISBN: 9781319309671

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 16.2, Problem 31E

To determine

To evaluate:

The given line integral over the line joining (0,0,0) and (1,4,4).

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Chapter 16.2, Problem 30E

Chapter 16.2, Problem 32E

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Chapter 16 Solutions

CALCULUS: EARLY TRANS 4TH ED W/ ACCESS

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The given line integral over the line joining ( 0 , 0 , 0 ) and ( 1 , 4 , 4 ) .

Solution Summary: The author explains how to evaluate the given line integral over the line joining (0,0-0).

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To evaluate:

The given line integral over the line joining (0,0,0) and (1,4,4).

Want to see the full answer?

Chapter 16 Solutions

The given line integral over the line joining ( 0 , 0 , 0 ) and ( 1 , 4 , 4 ) .

Solution Summary: The author explains how to evaluate the given line integral over the line joining (0,0-0).

Videos

To evaluate: The given line integral over the line joining (0,0,0) and (1,4,4).

Want to see the full answer?

Chapter 16 Solutions

To evaluate:

The given line integral over the line joining (0,0,0) and (1,4,4).