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An n-dimensional integral

  1. Dec 1, 2011 #1
    1. The problem statement, all variables and given/known data

    http://imageshack.us/photo/my-images/404/1322740516223.png/

    (http://imageshack.us/photo/my-images/404/1322740516223.png/)

    2. Relevant equations

    see image

    3. The attempt at a solution

    umm, I have no idea how to begin case n=2
     
  2. jcsd
  3. Dec 1, 2011 #2
    How about start with a plot? Then get rid of that ugly looking integral, then just focus entirely on n=2 like that's all you got to do.

    [tex]F_2(t)=\int_0^t\int_0^t f(\text{min}(x,y))dydx=\mathop\iint\limits_{\text{blue}} f(x)dydx+\mathop\iint\limits_{\text{red}} f(y)dydx[/tex]

    or is it the other way around? Need to check.
     

    Attached Files:

  4. Dec 1, 2011 #3
    Hmmm, so you split it into two integrals to cover both cases (f(x) or f(y) being the min value). Are all four bounds still 0 to t? And how should I go about finding the antiderivative of that expression as was done in case n=1. Does this require Green's theorem?
     
  5. Dec 1, 2011 #4
    What do you think? Come up with something. Show some work. That's a requirement in this sub-forum. Then try and post what you think are the limits using Latex. That the language we use in here to make nice math symbols. See:

    https://www.physicsforums.com/showthread.php?t=546968

    or just post them as text just to show you're trying. Or you can do a quote on my post to see how I coded the latex for that expression above. And I tell you what, suppose I have an integral function:

    [tex]f(t)=\int_a^t g(x,t)dx[/tex]

    how would I find f'(t)? Leibniz right?
     
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