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How do i maximize the line integral?

  1. Dec 12, 2009 #1
    suppose i have a nonconservative vector field.
    and there is a path going from point A to point B.
    How do i determine the path taken from A to B such that the line integral is maximized?
    edit: actually after thinkin about it, this might be an undefined problem unless there is some constraint on the x,y,z coordinates.
    Last edited: Dec 12, 2009
  2. jcsd
  3. Dec 12, 2009 #2


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    And on the length of the curve. Suppose a vector field circles the destination counterclockwise. What's to stop you from circling against the flow, round and round...
  4. Dec 13, 2009 #3


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    That is a "calculus of variations" problem. Do you know about the Euler-Lagrange equation?
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