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Calculating Moments

  1. Jul 3, 2008 #1
    Hi there...
    I'm not sure how to go about finding the following moments:

    M_{x}= \int \int\ [/tex] y dx dy
    M_{y}= \int \int\ [/tex] x dx dy

    Where the region is bounded by the ellipse:
    [tex]\frac{(x-2)^2}{16}} + \frac{(y-4)^2}{36}}[/tex] = 1

    I tried this several ways. I drew the ellipse and found the bounds to be
    -2 [tex]\leq y[/tex] [tex]\leq10[/tex]
    -2 [tex]\leq x[/tex] [tex]\leq 6[/tex]

    Then I tried integrating with those bounds, but I can't seem to get the right answers. Any help/hints would be greatly appreciated.
    Last edited: Jul 3, 2008
  2. jcsd
  3. Jul 3, 2008 #2
    Consider changing variables to center the ellipse around zero. eg:
    u = x - 2
    v = y - 4
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