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Greens theorem-help setting up correct integral

  1. Dec 9, 2008 #1
    1. The problem statement, all variables and given/known data
    Use Green Theorem to calculate [tex]\oint[/tex][tex]\widehat{}F[/tex] [tex]\bullet[/tex] d[tex]\widehat{}r[/tex] where C is the closed triangular curve oriented counterclockwise with verticies P1(0,5), P2(0,2) and P3(3,5). vectorF(x,y)= xy^2 i + 4xy j

    2. Relevant equations

    3. The attempt at a solution
    I first took the partial of F2 with respect to x = 4y
    partial of F1 with respect to y = 2xy

    [tex]\int[/tex][tex]\int[/tex]4y-2xy dA

    I am not sure of what limits to use:
    because it is oriented counter clockwise:
    y-2[tex]\leq[/tex] x [tex]\leq[/tex] 0
    5 [tex]\leq[/tex] y [tex]\leq[/tex] 2
  2. jcsd
  3. Dec 9, 2008 #2
    It looks fine except I would check your order of limits--it should be entering at [itex]x=0[/itex] and leaving at [itex]x=y-2[/itex] and it's backwards for y too--maybe that was just a mistake when you wrote it.
  4. Dec 10, 2008 #3
    that is how I did the problem initially however, the problem says it is in the counterclockwise direction which I would think y goes from 5 to 2, and x from 0 to y-2.
    (which is only half of what I did)

    Can anyone explain this?
  5. Dec 11, 2008 #4
    When you integrate a region, you do so on an interval [itex]x\in [a,b],y\in [c,d][/itex]. Does the integral make sense if [itex]a>b, c>d[/itex]?
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