Line integrals, often called path integrals, are a generalization of the idea of a definite integral from one variable calculus. There are two main ingredients in computing a line integral. The first is a vector field. This quantity often represents (in applications) a field of force, such as gravity or electricity, or a velocity field for a fluid. The second ingredient is a parameterized path. This path must be oriented. That is to say, there must be a direction off motion along the path which has been chosen as the positive direction. The line integral itself combines these ingredients to produce a single number which represents how much of the vector field is ``in the direction of'' the path.
