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Line integral help

  1. Mar 2, 2012 #1
    1. The problem statement, all variables and given/known data

    Trying to evaluate the following line integral:

    integral F ds where F = (6(x^2)(y^2), 4(x^3)(y) + 5y^4)
    and the path is the boundary curve of the first quadrant below y = 1-x^2 in a clockwise direction.

    2. Relevant equations

    3. The attempt at a solution

    So since the curve is piecewise smooth closed simple and closed curve I can use greens theorem. Simply put I get an answer as 0 since dF1/dy = dF2/dx. Is that right?
  2. jcsd
  3. Mar 2, 2012 #2


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    I would agree with that.
  4. Mar 2, 2012 #3
    Your vector field is conservative. So the line integral would be zero over any closed curve (even non-simple closed curve!). A vector field is conservative if it is the gradient of a potential function.
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