The Fundamental Theorem for Line Integrals

A line integral describes the accumulated contribution of a vector field along a curve connecting two points. It is used to evaluate how the direction and magnitude of a vector field interact with the direction of motion along a path. In certain cases, this calculation can be greatly simplified by identifying whether the vector field is associat...

A line integral measures how a vector field contributes along a curve from one point to another.

The Fundamental Theorem for Line Integrals applies when the vector field comes from a potential function.

In other words, the vector field F is the gradient of a potential function g of two or three variables.