A line integral is a mathematical concept used to calculate the integral of a function along a curve or path in space. It is particularly useful in physics and engineering for evaluating quantities like work done by a force along a path or the circulation of a vector field. The integral sums up the values of a function at each point along the curve, weighted by the length of the curve segment.
To compute a line integral, the curve is typically parameterized using a variable, often denoted as t. The function is then expressed in terms of this parameter, allowing the integral to be evaluated over a specified interval. Line integrals can be classified into two types: scalar line integrals, which involve scalar functions, and vector line integrals, which involve vector fields.