line integrals

(1.3 hours to learn)


The line integral gives a notion of integrating a vector field along a curve. Common uses include computing work done by a force and finding potential functions corresponding to a gradient field.


This concept has the prerequisites:


  • Be able to compute line integrals of vector fields with respect to curves
  • Be able to express the line integral in terms of the arc length parameterization, or in terms of an arbitrary parameterization
  • Why does the line integral of a vector field depend on the orientation of a curve?
  • Be aware that the line integrals are independent of the parameterization of a path, for a given orientation

Core resources (read/watch one of the following)


MIT Open Courseware: Multivariable Caclulus (2010)


See also