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Line Integrals / Conservative Vector Fields

  1. Dec 4, 2009 #1
    1. The problem statement, all variables and given/known data

    [tex]F = < z^2/x, z^2/y, 2zlog(xy)>[/tex]
    [tex]F = \nabla f[/tex], where [tex]f = z^2log(xy)[/tex]

    2. Relevant equations

    Evaluate [tex]\int F \cdot ds [/tex] for any path c from [tex] P = (1/2, 4, 2) [/tex] to [tex] Q = (2, 3, 3) [/tex] contained in the region [tex] x > 0, y > 0, z > 0 [/tex]

    Why is it necessary to specify that the path lie in the region where [tex] x, y, z [/tex] are positive?

    3. The attempt at a solution

    I did [tex] f(2,3,3) - f(1/2,4,2) [/tex] to get [tex] 9*log(6) - 4*log(2) [/tex]

    I don't really have an idea of how to answer the second question. Does it have to do with closed paths?
     
    Last edited: Dec 4, 2009
  2. jcsd
  3. Dec 5, 2009 #2
    think about the domain of the log function.
     
  4. Dec 5, 2009 #3

    lanedance

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    or the first 2 elements of F
     
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