1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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]?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook