Greens theorem-help setting up correct integral

  • Thread starter hils0005
  • Start date
  • #1
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Homework Statement


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


Homework Equations





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
 

Answers and Replies

  • #2
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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.
 
  • #3
62
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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?
 
  • #4
135
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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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