Explanation Given information: The given field is F = 〈 1 + x 2 , x y 2 〉 and the given curve is a line segment from ( 0 , 0 ) to ( 1 , 3 ) . Concept used: The line integral of the given vector field F = f 1 i + f 2 j over the curve C is given by ∫ C F ⋅ d r = ∫ a b F ( r ( t ) ) ⋅ r ' ( t ) d t where r ( t ) is the parametrization of the given curve C. Calculation: As given F = 〈 1 + x 2 , x y 2 〉 , first we parameterize the given curve which is a line segment from ( 0 , 0 ) to ( 1 , 3 ) as r ( t ) = ( 1 − t ) ( 0 , 0 ) + t ( 1 , 3 ) = 〈 t , 3 t 〉 ; 0 ≤ t ≤ 1 Thus, F ( r ( t ) ) = 〈 1 + ( t ) 2 , ( t ) ( 3 t ) 2 〉 = 〈 1 + t 2 , 3 t 3 〉

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 17.2, Problem 19E

To determine

To find: The line integral ∫CF⋅dr over the line segment from (0,0) to (1,3) .

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Chapter 17.2, Problem 18E

Chapter 17.2, Problem 20E

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Chapter 17 Solutions

CALCULUS (CLOTH)

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The line integral ∫ C F ⋅ d r over the line segment from ( 0 , 0 ) to ( 1 , 3 ) .

Solution Summary: The author explains that the line integral of the given vector field F=langle 1+x2,x

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To find: The line integral ∫CF⋅dr over the line segment from (0,0) to (1,3) .

Want to see the full answer?

Chapter 17 Solutions