   Chapter 13.3, Problem 5E

Chapter
Section
Textbook Problem

# Find the length of the curve.5. r(t) = i + t2 j + t3 k, 0 ≤ t ≤ 1

To determine

To find: The length of the curve L for the vector equation r(t)=i+t2j+t3k,0t1 .

Explanation

Given data:

r(t)=i+t2j+t3k,0t1

Formula used:

Write the expression to find length of the curve L for the vector r(t) .

L=ab|r(t)|dt (1)

Here,

r(t) is the tangent vector, which is the derivative of vector r(t) , and

[a,b] is parameter interval.

Find the tangent vector r(t) by differentiating each component of the vector r(t) as follows.

ddt[r(t)]=ddt[i+t2j+t3k]

r(t)=ddt(i)+ddt(t2j)+ddt(t3k) (2)

Write the following formula to compute the expression for r(t) .

ddt(t2)=2tddt(t3)=3t2ddt(constant)=0

Apply the corresponding formula in equation (2) to find r(t) .

r(t)=0+2tj+3t2k

r(t)=2tj+3t2k (3)

Take magnitude on both sides of equation (3)

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Find the mean for the following set of scores: 2, 7, 9, 4, 5, 3, 0, 6

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

#### For and , a × b =

Study Guide for Stewart's Multivariable Calculus, 8th

#### True or False: The x-intercepts are the values of x for which f(x) = 0.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 