Explanation Given information: A curve C is specified by C : line segment from ( 0 , 0 ) to ( 1 , 3 ) A vector valued function F ( x , y ) = 〈 1 + x 2 , x y 2 〉 Formula used: Suppose that curve C is the line joining two points ( x 0 , y 0 ) and ( x 1 , y 1 ) 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 And r ( t ) = ( 1 − t ) ( x 0 , y 0 ) + t ( x 1 , y 1 ) and 0 ≤ t ≤ 1 Calculation: Consider the given points ( 0 , 0 ) and ( 1 , 3 ) . Here, ( x 0 , y 0 ) = ( 0 , 0 ) and ( x 1 , y 1 ) = ( 1 , 3 ) C : r ( t ) = ( 1 − t ) ( 0 , 0 ) + t ( 1 , 3 ) and 0 ≤ t ≤ 1 Parameterized the curve by considering the following

CALCULUS EARLY TRANSCENDENTALS W/ACHIEVE

4th Edition

ISBN: 9781319057664

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 16.2, Problem 19E

To determine

To evaluate:

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

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Chapter 16.2, Problem 18E

Chapter 16.2, Problem 20E

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Chapter 16 Solutions

CALCULUS EARLY TRANSCENDENTALS W/ACHIEVE

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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Prob. 23CRE Ch. 16 - Prob. 24CRE Ch. 16 - Prob. 25CRE Ch. 16 - Prob. 26CRE Ch. 16 - Prob. 27CRE Ch. 16 - Prob. 28CRE Ch. 16 - Prob. 29CRE Ch. 16 - Prob. 30CRE Ch. 16 - Prob. 31CRE Ch. 16 - Prob. 32CRE Ch. 16 - Prob. 33CRE Ch. 16 - Prob. 34CRE Ch. 16 - Prob. 35CRE Ch. 16 - Prob. 36CRE Ch. 16 - Prob. 37CRE Ch. 16 - Prob. 38CRE Ch. 16 - Prob. 39CRE Ch. 16 - Prob. 40CRE Ch. 16 - Prob. 41CRE Ch. 16 - Prob. 42CRE Ch. 16 - Prob. 43CRE Ch. 16 - Prob. 44CRE Ch. 16 - Prob. 45CRE Ch. 16 - Prob. 46CRE Ch. 16 - Prob. 47CRE Ch. 16 - Prob. 48CRE Ch. 16 - Prob. 49CRE Ch. 16 - Prob. 50CRE Ch. 16 - Prob. 51CRE Ch. 16 - Prob. 52CRE Ch. 16 - Prob. 53CRE Ch. 16 - Prob. 54CRE Ch. 16 - Prob. 55CRE Ch. 16 - Prob. 56CRE Ch. 16 - Prob. 57CRE Ch. 16 - Prob. 58CRE Ch. 16 - Prob. 59CRE Ch. 16 - Prob. 60CRE Ch. 16 - Prob. 61CRE

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The integral ∫ C F ⋅ d r for the oriented curve specified.

Solution Summary: The author evaluates the integral of displaystyleundersetCintFcdot dr for the oriented curve.

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To evaluate:

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

Want to see the full answer?

Chapter 16 Solutions

The integral ∫ C F ⋅ d r for the oriented curve specified.

Solution Summary: The author evaluates the integral of displaystyleundersetCintFcdot dr for the oriented curve.

Concept explainers

Videos

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

Want to see the full answer?

Chapter 16 Solutions

To evaluate:

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