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Help with path integral

  1. Feb 17, 2012 #1
    1. The problem statement, all variables and given/known data


    The problem asks:

    find the integral of gamma F.ds where F(x,y,z) = (e^z, e^y, x+y).
    gamma being a triangle with vertices:

    (1,0,0) (0,1,0) (0,0,1) going in a counterclockwise direction

    2. Relevant equations



    3. The attempt at a solution

    So I'm not even sure if what I'm doing is right. This is my attempt to parameterize

    C1: x = t, y = 1-t, z = 0 for 0<t<1
    C2: x = 2-t, y = 0, z = 1-t for 1<t<2
    C3: x = 0, y = t-2, z = 3-t for 2<t<3

    And to find the integral it's

    F(c(t))*c'(t) dt

    is that right?
     
  2. jcsd
  3. Feb 17, 2012 #2
    It should be:
    ##C_1:\vec r=(1-t,t,0),0\le t\le1.##
    ##C_2:\vec r=(0,1-t,t),0\le t\le1.##
    ##C_3:\vec r=(t,0,1-t),0\le t\le1.##
     
  4. Feb 17, 2012 #3

    ehild

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    Homework Helper
    Gold Member

    Make a drawing, and show which lines are C1,C2,C3.

    ehild
     
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