Download the App!

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

Question

Answered step-by-step

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

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Keran Li

Numerade Educator

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

01:01

Amrita Bhasin

04:06

Mutahar Mehkri

Calculus 2 / BC

Chapter 6

Applications of Integration

Section 5

Average Value of a Function

Campbell University

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

Lectures

0:00

The linear density in a ro…

06:18

03:34

The linear density in an 8…

03:10

The linear density of a ro…

00:47

$\begin{array}{l}{\text { …

01:06

01:08

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.

View More Answers From This Book

Find Another Textbook