Hey, I am wondering if anyone can help me understand a mathematical explanation as to how they work. From what I understand, the area under a closed curve is the same, independent of the path taken. So when doing an integral you only need to take the initial and final into account. There have been 2 a few situations so far when I have come across these curves. Particularly when dealing with conservative forces, i.e. Gravity, Electricity. So with these forces, it is saying the work done is the same independent of the part taken. But what actually makes it a closed curve? What part of it all makes it so the path does not matter when getting the area under the curve?