Okay, I've searched PF. I actually found a thread that confirmed some of my assumptions. I've searched the web. But I still want to know what the geometric interpretation of a line integral with respect to x (or y) is. The example that made me want to know was [tex] \int y^2 dx + x dy [/tex]; It was integrated over the curve which is actually a line segment that goes from (-5,-3) to (0,2). I got the answer -5/6 by converting both variables into one and using the Jacobian. What bothers me is I don't know what that -5/6 means! It has to mean something.