How would you calculate this? Since $\textbf{F}$ has to be parametrized, could $(x=t)$ be used? And what about $y$ and $z$? Or, since the curve is a closed path, is it automatically zero?
Thanks.
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Split the curve into sum of 3 simple curves and parametrize each separately.
PS: I don't see why the path is closed. Start and end points are different.
Piotr Miś
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So is it 3 curves? Or does the last one go back to the starting point? If it's a polygon, doesn't that mean they are connected? – user7000 May 24 '14 at 16:50
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Well, that really depends on your definition of a polygonal path. I don't think they have to be closed. And yes, it's 3 segments. – Piotr Miś May 24 '14 at 16:51
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OK thank you. So I would just do the three curves separately and add them together? – user7000 May 24 '14 at 16:53
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Yes, exactly like that. There are other ways if you are interested. – Piotr Miś May 24 '14 at 16:55
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What else would work? :) Thanks. – user7000 May 24 '14 at 17:11
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For some 3D line integrals it is easier to use Stokes' theorem in order to express the problem as an evaluation of surface integral. I don't think it's a viable option here, though. :) – Piotr Miś May 24 '14 at 17:16