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Multivariable Version of FToC?

  1. May 19, 2015 #1
    So for a function of a single variable

    gif.latex?%5Cint_%7Ba%7D%5E%7Bb%7Ddf%3Df%28b%29-f%28a%29.gif

    How can this be extended to the integration of the total differential of a multivariable function over a region (specifically one of two variables)?
    That is, how do you integrate

    %20f%20%7D%7B%5Cpartial%20x%7Ddx%20+%20%5Cfrac%7B%5Cpartial%20f%20%7D%7B%5Cpartial%20y%7Ddy.gif

    Say over the circular region

    gif.gif , gif.gif
     
  2. jcsd
  3. May 19, 2015 #2

    hunt_mat

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    Homework Helper

    The generalisation to this to an arbitrary number of dimensions is Stokes' theorem.
     
  4. May 19, 2015 #3
    Ah, thanks. I guess I'm going to have to get off my ass and finish that MIT OCW Multivariable Calculus course I've been studying. I'm about halfway through, so I've seen double integrals and differentials, but not stoke's theorem.
     
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