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Homework Help: Solving double integral without integrating

  1. Apr 28, 2007 #1
    From an example in my book:

    Int Int (2x) dxdy over R = 0

    (R is the circe x^2+(y-1)^2=1)

    How can one make this conclusion without integrating?
     
  2. jcsd
  3. Apr 28, 2007 #2

    HallsofIvy

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    Look at the symmetry. A circle is "symmetric about the origin": If (x,y) is in the circle then so is (-x, -y). That means that for each possible x value, you have the corresponding -x and so the "effect" of the two points will cancel out.
     
    Last edited by a moderator: Apr 28, 2007
  4. Apr 28, 2007 #3

    Office_Shredder

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    It's actually symmetric about (0,1), but you can draw a similiar conclusion to HallsofIvy's post
     
  5. Apr 28, 2007 #4

    HallsofIvy

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    Right, sorry about that! If (x. 1+y) is in the circle, so is (-x, 1- y)!
     
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