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True or false questions about line/surface integral

  1. Dec 1, 2009 #1
    1. The problem statement, all variables and given/known data
    if f has a continuous partial derivatives on R^3 and c is any circle ,then the integral of gradient f dot dr over c is zero

    integral of f(x,y) ds over -c= - integral of f(x,y) ds over c

    2. Relevant equations

    3. The attempt at a solution

    if the condition is not mentioned, then that statement is usually wrong
    so i guess the second one is wrong
    not quite sure about the first one
  2. jcsd
  3. Dec 2, 2009 #2


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    Science Advisor

    For (1), think about "Green's theorem". Does it apply here?

    For (2), the "conditions" are that the function be integrable. Which it is because the question give [itex]\int f(x) dx[/itex].
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