edited 6th Dec '09 11:21:53 PM by Mapi-chan
Consider the area which is being integrated. 0<x<1 and 0<y<x. This can be written as 0<y<x<1, or 0<y<1 and y<x<1. Thus, we get the second integral being the same as the first. (I think I might be violating mathematical rigor in switching integrals at all, but you're an engineer so you don't need to worry about that—only crazy math majors like me have to worry about rigor.) Basically, write things in terms of a<x<b, where a and b can be based on the variables on the integrals outside of the one with that variable but not on those inside. Hopefully what I'm saying actually makes sense.
edited 6th Dec '09 11:34:12 PM by WilliamWideWeb
edited 6th Dec '09 11:42:32 PM by Mapi-chan
edited 6th Dec '09 11:42:47 PM by WilliamWideWeb
edited 6th Dec '09 11:49:37 PM by WilliamWideWeb
edited 6th Dec '09 11:55:52 PM by Mapi-chan
edited 7th Dec '09 12:01:42 AM by Mapi-chan
So yeah, Gaussian curvature indeed. Although in class, we defined it as D = E(8.854 x 10^-12 F/m) or epsilon sub-zero, but we retain the surface integral as dS.
edited 7th Dec '09 12:17:26 AM by Mapi-chan
edited 7th Dec '09 12:42:17 PM by Hydrall
edited 8th Dec '09 9:12:20 AM by Fawriel
edited 8th Dec '09 5:31:14 PM by Deboss
edited 8th Dec '09 5:56:29 PM by Ronka87