Solved

What can and cannot be integrated?

Posted on 2006-07-12
3
545 Views
Last Modified: 2012-08-13
Am I correct to believe that there are certain techniques to identify functions that cannot be integrated indefinitely?

If so: can someone please explain what they are?


Thanks
(Points will be upped if there is a solution)
0
Comment
Question by:InteractiveMind
  • 2
3 Comments
 
LVL 27

Accepted Solution

by:
aburr earned 50 total points
ID: 17091496
There are at leaast two different types of intergals. Riemann and Labegue.
They have different criteria as to the existance of the integral. All functions which are Legesque integrable are Riemann integrable but not vice versa.
Riemann is the most common. If the function is at least peicewise continuous, the definite integral exists. If you want the indefinite integral of an otherwise integable function you have to consider the end points. If one or the other approches infinity too rapidly you are in trouble.
If the function is not continuous (goes to infinity somewhere) it may still be integrable by Riemann techniques. There are various liniting procescess whihc can be used to check for integrableness. See textbooks.
0
 
LVL 84

Assisted Solution

by:ozo
ozo earned 50 total points
ID: 17092782
f(x) = 1 when x is rational, 0 when x is irrational, is Lebesgue integrable but not Riemann integrable
0
 
LVL 84

Assisted Solution

by:ozo
ozo earned 50 total points
ID: 17105905
And here's an example of a set that's not Lebesgue integrable http://en.wikipedia.org/wiki/Banach-Tarski_Paradox
0

Featured Post

Top 6 Sources for Identifying Threat Actor TTPs

Understanding your enemy is essential. These six sources will help you identify the most popular threat actor tactics, techniques, and procedures (TTPs).

Join & Write a Comment

Suggested Solutions

Introduction On a scale of 1 to 10, how would you rate our Product? Many of us have answered that question time and time again. But only a few of us have had the pleasure of receiving a stack of the filled out surveys and being asked to do somethi…
How to Win a Jar of Candy Corn: A Scientific Approach! I love mathematics. If you love mathematics also, you may enjoy this tip on how to use math to win your own jar of candy corn and to impress your friends. As I said, I love math, but I gu…
Access reports are powerful and flexible. Learn how to create a query and then a grouped report using the wizard. Modify the report design after the wizard is done to make it look better. There will be another video to explain how to put the final p…
This video gives you a great overview about bandwidth monitoring with SNMP and WMI with our network monitoring solution PRTG Network Monitor (https://www.paessler.com/prtg). If you're looking for how to monitor bandwidth using netflow or packet s…

760 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question

Need Help in Real-Time?

Connect with top rated Experts

25 Experts available now in Live!

Get 1:1 Help Now