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

See similar textbooks

Concept explainers

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magn…

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.

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.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 10.8, Problem 7E

Chapter 10.8, Problem 10E

Students have asked these similar questions

2 x² + 9 d x 1 x +9 dx

How did you get a(k+1) term?

Please answer it all and show all the work and steps on answer the questions

Chapter 10 Solutions

Essential Calculus: Early Transcendentals

Ch. 10.1 - Suppose you start at the origin, move along the...Ch. 10.1 - Sketch the points (0, 5, 2), (4, 0, 1), (2, 4, 6),...Ch. 10.1 - Which of the points A(4, 0, 1), B(3, 1, 5), and...Ch. 10.1 - Prob. 4E Ch. 10.1 - (a) What does the equation x = 4 represent in 2?...Ch. 10.1 - Describe and sketch the surface in 3 represented...Ch. 10.1 - Prob. 7E Ch. 10.1 - Determine whether the points lie on a straight...Ch. 10.1 - Find the distance from (4, 2, 6) to each of the...Ch. 10.1 - Find an equation of the sphere with center (2, 6,...

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

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).

Concept explainers

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.

Want to see the full answer?

Chapter 10 Solutions