Results 1 to 2 of 2

Thread: The method of exausted in double integrals

  1. #1
    Junior Member
    Joined
    Dec 2008
    From
    Tel Aviv
    Posts
    35

    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
    10
    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: Jan 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: Oct 30th 2008, 08:11 AM
  5. double integrals
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Oct 13th 2008, 09:20 AM

Search Tags


/mathhelpforum @mathhelpforum