# Convert line integral to surface integral

• Jan 31st 2013, 12:50 PM
sox1988
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!
• Jan 31st 2013, 12:58 PM
HallsofIvy
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.
• Jan 31st 2013, 01:19 PM
sox1988
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.
• Feb 1st 2013, 06:03 AM
sox1988
Re: Convert line integral to surface integral
I solved this problem with divergence theorem.
• Feb 1st 2013, 07:26 AM
HallsofIvy
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.
• Feb 2nd 2013, 03:18 PM
sox1988
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.