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Independence of parametrizations of a line integral

  1. Apr 10, 2012 #1
    1. The problem statement, all variables and given/known data
    I've been trying to prove a problem.
    I attach the problem. I refer to the book " Advanced calculus" written by watson fulks.
    You can find the below information in p. 405~p.417
    smooth curve(1).jpg
    line integral(2).jpg
    independence of parametrization(3).jpg
    I wanna prove C Exercise problem number 2.

    2. Relevant equations

    3. The attempt at a solution
    I could prove it when two parametrizations of a curve are bijective. But, I don't have any idea to access how to prove it in general. I even don't know whether the statement in C Exercise 2 is true or not...
    Is the statement true??
    Then, could you give me a hint??
    Last edited: Apr 10, 2012
  2. jcsd
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