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Double integral over region surrounded by two ellipses

  1. Apr 14, 2012 #1
    1. The problem statement, all variables and given/known data

    A thin plate has the form of the intersection of the regions limited by [itex]\frac{x^2}{9}[/itex] + [itex]\frac{y^2}{4}[/itex] = 1 and [itex]\frac{x^2}{4}[/itex] + [itex]\frac{y^2}{9}[/itex] = 1

    Which is the plate's mass if his density is δ(x, y) = |x|


    2. The attempt at a solution

    I've tried using u, v substitution

    u = [itex]\frac{x^2}{4}[/itex] + [itex]\frac{y^2}{9}[/itex]

    v = [itex]\frac{x^2}{9}[/itex] + [itex]\frac{y^2}{4}[/itex]

    The resulting region looks nice, but the Jacobian is the ugly thing... i'm stuck.

    I don't think polar is the way to go, one ellipse becomes a nice circle, but the other one becomes another ellipse....

    Can someone give me some advice?
    Thanks
     
  2. jcsd
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