Still celebrating National IT Professionals Day with 3 months of free Premium Membership. Use Code ITDAY17

x
?
Solved

What can and cannot be integrated?

Posted on 2006-07-12
3
Medium Priority
?
553 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
[X]
Welcome to Experts Exchange

Add your voice to the tech community where 5M+ people just like you are talking about what matters.

  • Help others & share knowledge
  • Earn cash & points
  • Learn & ask questions
  • 2
3 Comments
 
LVL 27

Accepted Solution

by:
aburr earned 200 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 200 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 200 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

Free Tool: Path Explorer

An intuitive utility to help find the CSS path to UI elements on a webpage. These paths are used frequently in a variety of front-end development and QA automation tasks.

One of a set of tools we're offering as a way of saying thank you for being a part of the community.

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

A Guide to the PMT, FV, IPMT and PPMT Functions In MS Excel we have the PMT, FV, IPMT and PPMT functions, which do a fantastic job for interest rate calculations.  But what if you don't have Excel ? This article is for programmers looking to re…
This article provides a brief introduction to tissue engineering, the process by which organs can be grown artificially. It covers the problems with organ transplants, the tissue engineering process, and the current successes and problems of the tec…
Although Jacob Bernoulli (1654-1705) has been credited as the creator of "Binomial Distribution Table", Gottfried Leibniz (1646-1716) did his dissertation on the subject in 1666; Leibniz you may recall is the co-inventor of "Calculus" and beat Isaac…
Finds all prime numbers in a range requested and places them in a public primes() array. I've demostrated a template size of 30 (2 * 3 * 5) but larger templates can be built such 210  (2 * 3 * 5 * 7) or 2310  (2 * 3 * 5 * 7 * 11). The larger templa…
Suggested Courses

722 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