Explanation Given: Curve = r ( t ) = 〈 4 t 1 2 , ln t , 2 t 〉 Point, a = 1 Formula used: s ( t ) = ∫ a t | | r ' ( u ) | | d u Calculation: r ' ( t ) = 〈 4 × 1 2 × t − 1 2 , 1 t , 2 〉 = 〈 2 t − 1 2 , 1 t , 2 〉 | | r ' ( t ) | | = ( 2 t − 1 2 ) 2 + ( 1 t ) 2 + ( 2 ) 2 = 4 t − 1 + 1 t 2 + 4 = 4 t + 1 t 2 + 4 = 4 t + 1 + 4 t 2 t 2 = ( 1 ) 2 + ( 2 t ) 2 + 2 × 2 t t 2 = ( 1 + 2 t ) 2 t 2 &#

Loose-Leaf Version for Calculus: Early Transcendentals Single Variable

4th Edition

ISBN: 9781319312886

Author: Rogawski, Jon, Adams, Colin, FRANZOSA, Robert

Publisher: W. H. Freeman

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 13.3, Problem 12E

To determine

Compute the arc length of the curve 〈4t12,lnt,2t〉.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.3, Problem 11E

Chapter 13.3, Problem 13E

Students have asked these similar questions

Let X be a random variable with the standard normal distribution, i.e.,X has the probability density functionfX(x) = 1/√2π e^-(x^2/2)2 .Consider the random variablesXn = 20(3 + X6) ^1/2n e ^x^2/n+19 , x ∈ R, n ∈ N.Using the dominated convergence theorem, prove that the limit exists and find it limn→∞E(Xn)

Let X be a discrete random variable taking values in {0, 1, 2, . . . }with the probability generating function G(s) = E(sX). Prove thatVar(X) = G′′(1) + G′(1) − [G′(1)]2.[5 Marks](ii) Let X be a random variable taking values in [0,∞) with proba-bility density functionfX(u) = (5/4(1 − u^4, 0 ≤ u ≤ 1,0, otherwise. Let y =x^1/2 find the probability density function of Y

2. y 1 Ο 2 3 4 -1 Graph of f x+ The graph gives one cycle of a periodic function f in the xy-plane. Which of the following describes the behavior of f on the interval 39 x < 41 ? (Α B The function f is decreasing. The function f is increasing. The function f is decreasing, then increasing. D The function f is increasing, then decreasing.

Chapter 13 Solutions

Loose-Leaf Version for Calculus: Early Transcendentals Single Variable

Ch. 13.1 - Prob. 1PQ Ch. 13.1 - Prob. 2PQ Ch. 13.1 - Prob. 3PQ Ch. 13.1 - Prob. 4PQ Ch. 13.1 - Prob. 5PQ Ch. 13.1 - Prob. 6PQ Ch. 13.1 - Prob. 1E Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - 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.

Compute the arc length of the curve 〈 4 t 1 2 , ln t , 2 t 〉 .

Concept explainers

Videos

Compute the arc length of the curve 〈4t12,lnt,2t〉.

Want to see the full answer?

Chapter 13 Solutions