Explanation Formula used: d s = ‖ r ′ ( t ) ‖ d t ∫ C f ( x , y , z ) d s = ∫ t = a b f ( r ( t ) ) ‖ r ′ ( t ) ‖ d t Calculations: Given f ( x , y , z ) = x + 2 y + z and r ( t ) = 〈 cos t , sin t , t 〉 for 0 ≤ t ≤ π 2 Since r ( t ) = 〈 cos t , sin t , t 〉 , so x = cos t , y = sin t , z = t Thus, f ( x , y , z ) = x + 2 y + z f ( r ( t ) ) = cos t + 2 sin t + t Now, since r ( t ) = 〈 cos t , sin t , t 〉 , so r ′ ( t ) = 〈 − sin t , cos t , 1 〉 Hence, ‖ r ′ ( t ) ‖ = ( − sin t ) 2 + ( cos t ) 2 +

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 17, Problem 31CRE

To determine

To compute the line integral:

$f (x, y, z) = x + 2 y + z$ , the helix $r (t) = 〈 \cos t, \sin t, t 〉 for 0 \leq t \leq \frac{π}{2}$

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Chapter 17, Problem 30CRE

Chapter 17, Problem 32CRE

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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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To compute the line integral: f ( x , y , z ) = x + 2 y + z , the helix r ( t ) = 〈 cos t , sin t , t 〉 for 0 ≤ t ≤ π 2

Solution Summary: The author explains how the helix r (t) = cos t, sin

Concept explainers

Videos

To compute the line integral:

$f (x, y, z) = x + 2 y + z$ , the helix $r (t) = 〈 \cos t, \sin t, t 〉 for 0 \leq t \leq \frac{π}{2}$

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Chapter 17 Solutions

To compute the line integral: f ( x , y , z ) = x + 2 y + z , the helix r ( t ) = 〈 cos t , sin t , t 〉 for 0 ≤ t ≤ π 2

Solution Summary: The author explains how the helix r (t) = cos t, sin

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To compute the line integral: f(x,y,z)=x+2y+z, the helix r(t)=〈cost,sint,t〉 for 0≤t≤π2

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Chapter 17 Solutions

To compute the line integral:

$f (x, y, z) = x + 2 y + z$ , the helix $r (t) = 〈 \cos t, \sin t, t 〉 for 0 \leq t \leq \frac{π}{2}$