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Using Green's Theorem for Vector Fields

  1. Apr 11, 2015 #1
    1. The problem statement, all variables and given/known data
    Picture1.png

    2. Relevant equations
    n/a

    3. The attempt at a solution
    I don't understand how the book went from calculating Green's theorem on ##\int _c Pdx + Qdy + \int _{-c'} Pdx + Qdy = ## (1 in the attached picture) to getting (labeled 2) ##\int _c Pdx + Qdy = \int _{c'} Pdx + Qdy ##

    Thank you
     
  2. jcsd
  3. Apr 11, 2015 #2
    just work out the derivatives ##\frac{\partial Q}{\partial x}## & ##\frac{\partial P}{\partial y}## & use the fact that for a path C, ##\int_{-C} P\,dx + Q\,dy = -\int_{C} P\,dx + Q\,dy##
     
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