Results 1 to 1 of 1

Math Help - multiple integration question

  1. #1
    Newbie
    Joined
    May 2010
    Posts
    1

    multiple integration question

    If f(x,y) is nonnegative decrasing in x for fixed y, 0<x<1, 0<y<0.4 say, then one can show that the quadruple integral

    <br />
\int_{0}^{u} \int_{u}^{1} \int_{0}^{0.4} \int_{0}^{0.4} (f(x,y)-f(x',y')) dy dy' dx dx' \leq 0 .

    Is it true that

    <br />
\int_{0}^{u} \int_{u}^{1} \int_{0}^{0.4} \int_{0}^{0.4} g(x,y) g(x',y') [f(x,y)-f(x',y')] dy dy' dx dx' \leq 0 .


    for any non-negative function g(x,y) ? I think it is but can't seem to come up with a simple proof without going through the process of simple functions etc. Other assumptions are

    f and g are bounded by 1, continously differentiable with respect to each parameter.

    Thanks,
    Last edited by salem1; May 14th 2010 at 01:12 PM. Reason: there was a typor, second integral is from u to 1
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Multiple Integration
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 19th 2010, 04:13 AM
  2. General multiple integration question
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 14th 2010, 06:52 PM
  3. Replies: 3
    Last Post: March 28th 2009, 07:27 AM
  4. Multiple integration help......
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 28th 2008, 04:45 AM
  5. Multiple integration + Centroids Question
    Posted in the Calculus Forum
    Replies: 0
    Last Post: November 24th 2007, 10:06 AM

Search Tags


/mathhelpforum @mathhelpforum