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: 9781319055844

Author: FRANZOSA

Publisher: VST

See similar textbooks

Concept explainers

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the se…

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integratio…

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects th…

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.

Videos

Question

Chapter 14.3, Problem 11E

To determine

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

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.3, Problem 10E

Chapter 14.3, Problem 12E

Students have asked these similar questions

Plot the curve c(t) = (cos t, esin t ) for 0 ≤ t ≤ 2π

The curves F₁ (t) = (2 sin(t), 4 cos(t), e¹) and 72(t) = (3 ln(t), 4√t, t³) intersect at the point (0, 4, 1). Find the angle of intersection, in radians on the domain 0 ≤ 0≤, to two decimal places. Submit Question

A glider is soaring upward along the helix r(t) = (cos t)i + (sin t)j + tk. How long is the glider’s path from t = 0 to t = 2π?

Chapter 14 Solutions

EBK CALCULUS

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

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 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.

Concept explainers

Videos

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

Want to see the full answer?

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.

Concept explainers

Videos

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

Want to see the full answer?

Chapter 14 Solutions

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