let C be a smooth simple closed curve in the plane and n be a unit vector normal to C.

prove that the integral of n.ds over C is 0.

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- December 1st 2008, 06:18 PMlauren2988flux and integrals over a closed surface
let C be a smooth simple closed curve in the plane and n be a unit vector normal to C.

prove that the integral of n.ds over C is 0. - December 1st 2008, 07:53 PMThePerfectHacker
You cannot compute a line integral over a vector field. (Surprised)

Therefore the integral of n.ds over just makes no sense.

I think you might mean the following:

Define the vector-field by .

From here we see that and (sum of components of the normal vector).

Thus, by divergence theorem,