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Homework Help: Help on easy integration

  1. Feb 13, 2007 #1
    1. The problem statement, all variables and given/known data
    I want to perform the following integration:
    double integral of [(x^2)-(y^2)+2] dxdy where the function is subjected to the bound (x^2)+(y^2) greater than or equal to 2.

    I'm trying to find the flux of a surface of a sphere (x^2)+(y^2)+(z^2)=9.

    2. Relevant equations
    Nothing, just rules of integration.

    3. The attempt at a solution
    Using Cartesian coordinates seems far too difficult. I could show you my work, but it's messy and complicated.
    If I use parametrisation, then I get
    double integral of [(r^2)cos^2(t)-(r^2)sin^2(t)+2) rdrdt
    what are the bounds though?
    t is between 0 and 2pi I'm pretty sure, but what about r?
    It seems difficult since x^2+y^2 is greater than or equal to 2. This means that r^2 is greater than or equal to 2. Thus, it seems sqrt(2) is a lower bound, but what would the upper bound be?

    Does this make any sense?
     
  2. jcsd
  3. Feb 22, 2007 #2
    For the trig part: Hint: http://www.sosmath.com/trig/Trig5/trig5/trig5.html
    However, considering the bound you stated, it looks like your integral diverges.
    If you integrate only where x>2 and y<1, you already get divergence.
    So, to answer your question: No.
     
    Last edited: Feb 22, 2007
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