Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Sent to:
Search glass icon
  • Login
  • Textbooks
  • Ask our Educators
  • Study Tools
    Study Groups Bootcamps Quizzes AI Tutor iOS Student App Android Student App StudyParty
  • For Educators
    Become an educator Educator app for iPad Our educators
  • For Schools

Problem

(a) A cup of coffee has temperature 95 $ ^\circ C…

01:58

Question

Answered step-by-step

Problem 19 Medium Difficulty

The linear density in a rod 8 m long is $ \frac{12}{\sqrt{x + 1}} $ kg/m, where $ x $ is measured in meters from one end of the rod.
Find the average density of the rod.


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

KL
Keran Li
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Keran Li

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

More Answers

01:01

Amrita Bhasin

04:06

Mutahar Mehkri

Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 6

Applications of Integration

Section 5

Average Value of a Function

Related Topics

Applications of Integration

Discussion

You must be signed in to discuss.
Top Calculus 2 / BC Educators
Anna Marie Vagnozzi

Campbell University

Kayleah Tsai

Harvey Mudd College

Kristen Karbon

University of Michigan - Ann Arbor

Samuel Hannah

University of Nottingham

Calculus 2 / BC Courses

Lectures

Join Course
Recommended Videos

0:00

The linear density in a ro…

06:18

The linear density in a ro…

03:34

The linear density in an 8…

03:10

The linear density of a ro…

00:47

$\begin{array}{l}{\text { …

01:06

The linear density of a ro…

01:08

The linear density of a ro…

Watch More Solved Questions in Chapter 6

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26

Video Transcript

So the resort is over 80 m. And the density function f. of X is equal to 12 over square root of X plus one. Now we want to find the average density now because we have the density function. So we can find the mass. Uh huh. The resort will be equal to the integral From 0- eight. The density function well over a squirrel or X plus one. The eggs. Yeah. Then for this function we can do a substitution with it. You equal to square root of X plus what? Then in this case we will find D. You equal to one half. Bye one over graduate of X plus one. Then we substitute this into the pentagram. And they the upper and lower bounds when X is equal to one we will have you equal sorry when X equal to zero we will have you equal to one. And when x equal to eight we will have you equal to three. Then back to well by because do you? Sorry? Here is the X. Now because D. U. Is equal to this guy by the eggs. So we will see one over root X plus one by T. X. Should be for +22 by D. You. So here it becomes 12 by two by D. You. Then for this one is just 24 by True which is 48. So this is a total mess. Then we want to find the average mass. So the average mass. Sorry the average density average Dennis A ticket. It will be equal to the total mass divided by the total length which is 48, Divided by eight, so it's equal to six.

Get More Help with this Textbook
James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups
Study with other students and unlock Numerade solutions for free.
Math (Geometry, Algebra I and II) with Nancy
Arrow icon
Participants icon
126
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
62
Hosted by: Alonso M
See More

Related Topics

Applications of Integration

Top Calculus 2 / BC Educators
Anna Marie Vagnozzi

Campbell University

Kayleah Tsai

Harvey Mudd College

Kristen Karbon

University of Michigan - Ann Arbor

Samuel Hannah

University of Nottingham

Recommended Videos

0:00

The linear density in a rod 8 m long is $ \frac{12}{\sqrt{x + 1}} $ kg/m, where…

06:18

The linear density in a rod $8 \mathrm{m}$ long is $12 / \sqrt{x+1} \mathrm{kg}…

03:34

The linear density in an 8m long metal rod is given by d(x) = 12/(sqrt(x+1)) wh…

03:10

The linear density of a rod of length $ 4 m $ is given by $ \rho (x) = 9 + 2 \s…

00:47

$\begin{array}{l}{\text { The linear density of a rod of length } 4 \mathrm{m} …

01:06

The linear density of a rod of length 1 $\mathrm{m}$ is given by $\rho(\mathrm…

01:08

The linear density of a rod of length $ 1\;m $ is given by $ p(x) = 1/\sqrt{x} …

Add To Playlist

Hmmm, doesn't seem like you have any playlists. Please add your first playlist.

Create a New Playlist

`

Share Question

Copy Link

OR

Enter Friends' Emails

Report Question

Get 24/7 study help with our app

 

Available on iOS and Android

About
  • Our Story
  • Careers
  • Our Educators
  • Numerade Blog
Browse
  • Bootcamps
  • Books
  • Notes & Exams NEW
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started