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Line integrals and paths with the same endpoints

  1. Feb 26, 2012 #1
    1. The problem statement, all variables and given/known data
    Suppose that p and q are points in U, where U is an open, path-connected, simply connected subset of Rn and c1 and c2 are smooth curves in Rn with c1(0)=c2(0)=p, c1(1)=c2(1)=q. Let w be a 1-form on U. Prove that the line integral of w over c1 equals the line integral of w over c2.


    2. Relevant equations
    simply connected means every closed curve homotopes to a point



    I don't know where to start :(
     
  2. jcsd
  3. Feb 26, 2012 #2

    Ray Vickson

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    Reading your textbook or lecture notes would be a good place to begin.

    RGV
     
  4. Feb 27, 2012 #3

    HallsofIvy

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    You might start with the definition of "one-form". And do you know what an "exact differential" is? It looks to me like the statement you are trying to prove is NOT true unless there are some other conditions.
     
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