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Homework Help: Gauss-Green Cardioid problem not coming out right

  1. Jul 15, 2012 #1
    1. The problem statement, all variables and given/known data
    Here is the region R plotted in the xy plane by the functions

    go with
    f(x,y)=3+y-x and g(x,y)=3-x

    calculate ∫∫_R f(x,y) dxdy and ∫∫_R g(x,y) dxdy

    2. Relevant equations

    3. The attempt at a solution
    I know I need to use the Gauss-Green formula so






    ∫(m(X(t),Y(t))X'(t)+n(X(t),Y(t))Y'(t)) dt from a to b

    Now I know this is a cardioid with a area of 3∏/2 but when I put everything in I get 18.06. Is my a and b wrong because I swear I have done everything else right
    Last edited by a moderator: Jul 15, 2012
  2. jcsd
  3. Jul 15, 2012 #2


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    The integral won't come out to be equal to the area of the cardioid. Why do you think it does? Your answer of 18.06 is correct.
  4. Jul 15, 2012 #3
    lol wow I feel stupid, its measuring a 3d space formed by the cardiod and the plane of f(x,y) and g(x,y). I get it now
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