2 Attachment(s)

Convert line integral to surface integral

Hello!

I have problem with converting line integral to surface integral of functions in polar coordinates.

Here are two examples

Attachment 26785

and

Attachment 26786

How can I convert this two line integrals to surface integrals.

w and v are functions w = w(r, phi) and v = v(r, phi)

Thanks for help!

Re: Convert line integral to surface integral

IF these are **closed** paths then you can convert to a surface integral over the region they bound, using Stoke's theorem. If they do not, you could "close" the paths in an infinite number of ways give different representations.

Re: Convert line integral to surface integral

I have a region from inner radius to outer radius and from lower angle to upper angle (region is a piece of circular ring) - two edges are at constant radius and two are at constant angle. Do you have any equation for Stoke's theorem in polar coordinates.

Re: Convert line integral to surface integral

I solved this problem with divergence theorem.

Re: Convert line integral to surface integral

Really? The divergence theorem relates the integral over a closed surface to the integral over the volume enclosed by the surface. That is not what you were asking about before.

Re: Convert line integral to surface integral

I found equation on this page http://www.calpoly.edu/~dhartig/Page...olarCoords.pdf and I got what I wanted.