I took multivariable calculus a while back. It was all fine until we got to line integrals and surface integrals divergance etc. Then it seemed like I got the rug swept from beneath me. After taking physics 2 alot of it makes so much more sense now though. Im reading through that stuff for a second time now, but am not sure about one thing for line integrals. I understand a line integral with respect to deltaS, or arc length. That can be visualized in terms of the area that the space curve "fence" so to speak makes on one side. But what in the heck is a line integral with respect to deltax, or deltay. They dont give you the same anwser as deltaS. I looked through 3 different books calc books, and not one of them goes into any detail about WHY we want to use these or what the hell they mean. So far im only left with my intution telling me that it may somehow be related to a projection onto the xz plane where y has no effect for the delta x, or similarly the yz plane where x has no effect for delta y, I don't, you all are smarter than me please help. The book does give some good examples of line integral applications in phyiscs, like center of mass of a wire, or the weight of a wire with varyin density, but all are with respect to deltaS, nothing to do with deltaX or deltaY!