Explanation Formula used: The length of the curve L for the vector r ( t ) is s ( t ) = ∫ a b | r ′ ( t ) | d t , r ′ ( t ) is the tangent vector and [ a , b ] is the parameter of the interval. Calculation: The given parametric curve is r ( t ) = 2 t i + ( 1 − 3 t ) j + ( 5 + 4 t ) k and the arc length measured from the point t = 0 . Compute the tangent vector r ′ ( t ) by differentiating each component of the vector r ( t ) as follows. d d t [ r ( t ) ] = d d t [ 2 t i + ( 1 − 3 t ) j + ( 5 + 4 t ) k ] r ′ ( t ) = d d t ( 2 t ) i + d d t ( 1 − 3 t ) j + d d t ( 5 + 4 t ) k = 2 i − 3 j + 4 k The magnitude of the tangent vector r ′ ( t ) can be obtained as follows. | r ′ ( t ) | = ( 2 ) 2 + ( − 3 ) 2 + ( 4 ) 2 = 4 + 9 + 16 = 29 Since the measure of arc length is from t = 0 , consider the tangent vector | r ′ ( t ) | = | r ′ ( u ) |

Essential Calculus: Early Transcendentals

2nd Edition

ISBN: 9781133112280

Author: James Stewart

Publisher: Cengage Learning

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Question

Chapter 10.8, Problem 9E

To determine

The arc length function by reparametrize curve for the curved measured equation r(t)=2ti+(1−3t)j+(5+4t)k from the point t=0.

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Chapter 10.8, Problem 7E

Chapter 10.8, Problem 10E

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Essential Calculus: Early Transcendentals

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The arc length function by reparametrize curve for the curved measured equation r ( t ) = 2 t i + ( 1 − 3 t ) j + ( 5 + 4 t ) k from the point t = 0 .

Solution Summary: The author calculates the arc length function by reparametrize curve for the given equation r(t).

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The arc length function by reparametrize curve for the curved measured equation r(t)=2ti+(1−3t)j+(5+4t)k from the point t=0.

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Chapter 10 Solutions