How do i maximize the line integral?

[okkvlt]

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.

 

[LCKurtz]

actually after thinkin about it, this might be an undefined problem unless there is some constraint on the x,y,z coordinates.

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...

 

[HallsofIvy]

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