I understand integrals but what are contour integrals?
2026-04-14 01:41:44.1776130904
What is the difference between integrals and contour integrals?
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Integrals, as you call them, and contour integrals are the same thing at a basic level: they are limits of certain sums over functions. The practical difference, however, is that the contour integral really represents one way, out of infinitely many, to integrate a function between 2 points, Point A and Point B, in a plane. The integral, on the other hand, has only one path by which to integrate from Point A to Point B.
Further, it makes sense to speak of closed contour integrals - well, OK, you could speak of integrating a function from Point A to Point B, and back again on the real line, but that isn't very interesting. On the other hand, you can speak of going from Point A to Point B along one path, and then from Point B back to Point A along a different path. In some cases, the net result is not zero. (In fact, it only is when the function in question is analytic on and within the contours.)