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Using Green's Theorem to evaluate the line integral.

  1. Nov 19, 2012 #1
    1. The problem statement, all variables and given/known data

    Green's Theorem to evaluate the line following line integral, oriented clockwise.
    ∫xydx+(x^2+x)dy, where C is the path though points (-1,0);(1,0);(0,1)

    2. Relevant equations
    Geen's theorem: [itex]∫F°DS=∫∫ \frac{F_2}{δx}-\frac{F_1}{δy}[/itex]


    3. The attempt at a solution
    attachment.php?attachmentid=53123&stc=1&d=1353355503.jpg

    What would I use for the bounds. I know it has to do with the triangle. But how would I find the bounds?
     

    Attached Files:

  2. jcsd
  3. Nov 19, 2012 #2

    HallsofIvy

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    You've pretty much written it down yourself: the lower limit is clearly y= 0. The upper limits are those two other sides of the triangle: if x< 0, y= x+ 1, if x> 0, y= -x+1.
    So you can divide this into two sets of integrals: for x from -1 to 1, y goes from 0 to x+ 1, for x from 0 to 1, y goes from 0 to 1- x.
     
  4. Nov 20, 2012 #3
    Thanks... Halls. I wasn't sure what to do, but I understand now. It's like you've divided the triangle into 2 pieces.
     
  5. Nov 20, 2012 #4
    And made both of the equations x+1 and 1-x satisfy their respective points... but I think the upper and lower bound of x+1 is -1 and 0 respectively since it goes from 0 to satisfy point (0,1) and -1 for (-1,0) and goes from the first point to the other.
     
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