Explanation Given information: A curve C is specified by Quarter of the circle of radius 2 in the y z plane with center at origin where y ≥ 0 and z ≥ 0 , oriented clockwise. A vector valued function F ( x , y , z ) = 〈 z 3 , y z , x 〉 Formula used: Suppose that curve Cis a parametric curve r ( t ) 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 Calculation: Here, radius is 2 and center is at origin. Let us consider the parametric equation for the portion of the curve C . x = 0 , y = 2 sin t , and z = 2 cos t such that 0 ≤ t ≤ π 2 C : r ( t ) = 〈 0 , 2 cos t , 2 sin t 〉 So, r ′ ( t ) = 〈 0 , − 2 sin t , 2 cos t 〉 Further calculate F ( r ( t ) ) as shown below. F ( r ( t ) ) = F ( 0 , 2 cos t , 2 sin t ) = 〈 8 sin 3 t , 4 cos t sin t , 0 〉 The value of the line integral can be calculated as shown below

4th Edition

ISBN: 9781319055905

Author: FRANZOSA

Publisher: VST

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Chapter 16.2, Problem 26E

To determine

To evaluate:

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

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Chapter 16.2, Problem 25E

Chapter 16.2, Problem 27E

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Chapter 16 Solutions

EBK CALCULUS: EARLY TRANSCENDENTALS

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

Solution Summary: The author evaluates the integral for the oriented curve C, based on the parametric equation r(t).

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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 for the oriented curve C, based on the parametric equation r(t).

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.