Thread: Simple Greene's Theorem Problem

Hi, I have what I think is a pretty simple Greene's theorem problem, but I can't seem to figure it out. Here's the problem:

D is a line segment joining (v1,u1) and (v2,u2). Show that Integral(-u dv + v du) = v1u2-v2u1

To do this, I tried employing Greene's theorem, and took the partials.
I then had the double integral of (1-(-1))dvdu, with bounds v1->v2 and u1->. However, that integrate does not come out to equal the proposed solution.

If someone could just tell me if I maybe I'm not supposed to be using Greene theorem or something like that, that would be a big help. Thanks!

is the line segment a simple closed curve in R2 ??
the curve should be closed see this
Green's theorem - Wikipedia, the free encyclopedia

Yes, it is closed and simple.