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Line integral along a path

  1. Apr 3, 2013 #1
    1. The problem statement, all variables and given/known data

    Vector field is F=-y[itex]\hat{x}[/itex] + x[itex]\hat{y}[/itex]

    Compute the line integral along the path c(t)=( cos(t), sin(t) ) with 0≤t≤∏


    2. The attempt at a solution
    i started computing f.dl but how much is dl ? I took it dx[itex]\hat{x}[/itex] +dy[itex]\hat{y}[/itex] i'm not sure if using Cartesian coordinates is right ?
     
  2. jcsd
  3. Apr 3, 2013 #2

    HallsofIvy

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    I can's see why you would say " i'm not sure if using Cartesian coordinates is right" when everything is given in Cartesian coordinates. You are given that the line is defined by [itex]c(t)= (cos(t), sin(t))[/itex] so it should be clear that [itex]dc= (-sin(t), cos(t))dt[/itex] and that is dl because it has unit length.
     
  4. Apr 3, 2013 #3
    Found it ! it's 0.5∏
     
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