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Green's theorem and area calculation

  1. Mar 5, 2014 #1
  2. jcsd
  3. Mar 5, 2014 #2

    SteamKing

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    Go back to the very definition of the Green's Theorem in the 'Theorem' section of the article. You pick M and N arbitrarily so that the equivalent double integral for the area of the region enclosed by the curve C can be expressed as a line integral around C. These choices of M and N are not necessarily unique.
     
  4. Mar 5, 2014 #3

    LCKurtz

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    If ##\vec F = \langle P(x,y),Q(x,y)\rangle## then Green's theorem is$$
    \iint_R Q_x - P_y~dA =\oint_C \vec F\cdot d\vec r$$If ##Q_x - P_y = 1## the double integral on the left gives the area of the enclosed region ##R##. Any choices of ##P## and ##Q## that give ##1## will work. The choices in your example are simple examples that work but you could likely find others.
     
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