Results 1 to 2 of 2

Math Help - The method of exausted in double integrals

  1. #1
    Junior Member
    Joined
    Dec 2008
    From
    Tel Aviv
    Posts
    29

    The method of exausted in double integrals

    We've learned about improper double integrals and I've a couple of questions :-)
    If a function is non-negative or non-positive then if we integrate it over an unbounded domain, the outcome won't depend on what type of exaustion we chose.. do you know what theorem is that ?
    I've tried to think a function that didn't satisfy that condition and its integration depends on the type of exaustion but I could think of one (is there a method for doing this?)

    thank you in advance
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    In the context of Lebesgue integration, the theorem is called Tonelli's theorem. That link also has an example of a function where iterated integrations lead to different results (but for an unbounded function over a bounded domain).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. double integrals
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 25th 2010, 02:05 PM
  2. Replies: 5
    Last Post: January 22nd 2010, 05:50 AM
  3. Double Integrals
    Posted in the Calculus Forum
    Replies: 5
    Last Post: May 4th 2009, 05:47 PM
  4. double integrals with e
    Posted in the Calculus Forum
    Replies: 4
    Last Post: October 30th 2008, 08:11 AM
  5. double integrals
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 13th 2008, 09:20 AM

Search Tags


/mathhelpforum @mathhelpforum