True or false questions about line/surface integral

  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. HallsofIvy

    HallsofIvy 41,265
    Staff Emeritus
    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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