Is the Line Integral Independent of the Path?

[aaronfue]

Homework Statement

Evalutate \int_{C} (y²-3x²)dx + (2xy+2)dy, where C is a smooth curve from (0,1) to (1,3).

2. The attempt at a solution

I've checked through my notes and text but can't find an example. I'd appreciate it if someone could help me get this started.

 

[clamtrox]

The problem seems to imply that the integral is independent of the path. Is this true in general, or is this some special case?

If the integral is indeed independent of the path, then one way of solving the problem is to just pick an arbitrary smooth path and calculate the integral. A straight line is probably the easiest.