   Chapter 13.3, Problem 1E

Chapter
Section
Textbook Problem

# Find the length of the curve.1. r(t) =⟨t, 3 cos t, 3 sin t⟩, − 5 ≤ t ≤ 5

To determine

To find: The length of the curve L for the vector equation r(t)=t,3cost,3sint,5t5 .

Explanation

Given data:

r(t)=t,3cost,3sint,5t5

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)]=ddtt,3cost,3sint

r(t)=ddt(t),ddt(3cost),ddt(3sint) (2)

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

ddtt=1ddt(cost)=sintddt(sint)=costddt(constant)=0

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

r(t)=ddt(t),ddt(3cost),ddt(3sint)

r(t)=1,3sint,3cost (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 more solutions based on key concepts 