Multivariable Calculus Books

Line integrals have a great many applications in the sciences, but were originally constructed mainly to compute work and mass in physics. Generally, if direction can be described along a curve using a parametric representation (called an orientable curve), then as a generalization of the Riemann integral it is possible to define a line integral where Riemann sums are constructed along the piecewise-smooth orientable curve. This topic illustrates how line integrals can be evaluated by reducing the line integral into a familiar one-variable integral with respect to the variable of parameterization of the piecewise-smooth orientable curve. Techniques for evaluating line integrals and applications are also detailed.