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Area of a Disk

  1. Apr 25, 2012 #1
    1. The problem statement, all variables and given/known data

    Suppose f : ℝ→ℝ and g : ℝ →ℝ are continuous. Suppose that f is odd and g is even. Define h(x,y) : f(x)*g(y).
    Let D be a disk centered at the origin in the plane. What is

    ∫∫h(x,y)dA?
    D


    3. The attempt at a solution
    I know there's probably a trick to it. Is it 0 because h becomes odd over a disk that is symmetrical to the origin?
     
    Last edited by a moderator: Apr 25, 2012
  2. jcsd
  3. Apr 25, 2012 #2

    Dick

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    Yes, that's basically it. Set it up as a dx*dy integral with limits if you want to show it explicitly.
     
  4. Apr 25, 2012 #3

    Dick

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    The problem posted was to evaluate the integral of h(x,y) over a disk D centered on the origin, where h(x,y)=f(x)g(y), f is an even function, g is odd.
     
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