Explanation r ( t ) = ( t 2 , 2 t 2 , t 3 ) N o w ∥ r ' ( t ) ∥ = 4 t 2 + 16 t 2 + 9 t 4 ∥ r ' ( t ) ∥ = t 20 + 9 t 2 To obtain ∥ r ' ( u ) d u ∥ we use the substitution method. Substitute u = 20 + 9 t 2 T h e n d u = 18 t d t t d t = 1 18 d u Now for the value of limit t = 0 u = 20 a n d t = t u = 20

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 14.3, Problem 11E

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The arc length function $s (t) = \int_{a}^{t} ∥ r' (u) ∥ d u$ for the given values of a.

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Chapter 14.3, Problem 10E

Chapter 14.3, Problem 12E

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Chapter 14 Solutions

CALCULUS (CLOTH)

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 6PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E

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The arc length function s ( t ) = ∫ a t ∥ r ' ( u ) ∥ d u for the given values of a.

Solution Summary: The author explains that the arc length function is given by s (t ) = 1 27 for the given values of a.

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The arc length function $s (t) = \int_{a}^{t} ∥ r' (u) ∥ d u$ for the given values of a.

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Chapter 14 Solutions

The arc length function s ( t ) = ∫ a t ∥ r ' ( u ) ∥ d u for the given values of a.

Solution Summary: The author explains that the arc length function is given by s (t ) = 1 27 for the given values of a.

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The arc length function s(t)=∫at∥r'(u)∥du for the given values of a.

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Chapter 14 Solutions

The arc length function $s (t) = \int_{a}^{t} ∥ r' (u) ∥ d u$ for the given values of a.