Multivariable Version of FToC?

  • Thread starter CSteiner
  • Start date
  • #1
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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
 

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  • #2
hunt_mat
Homework Helper
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The generalisation to this to an arbitrary number of dimensions is Stokes' theorem.
 
  • #3
31
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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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