Khan Academy: Vector Field Line Integrals Dependent on Path Direction

Video lesson using line integrals in a vector field for a path in opposite directions. Gives the intuition and then shows that the results will have opposite signs. [15:51]

Video lesson using line integrals to find the area along a parametric curve in both directions. Shows that the results are the same for either direction by using substitution. [16:22]

Using a line integral to find the work done by a vector field example.

Video lesson using a line integral to find the work done on a particle on a specific path in a specific vector field. Solution results in negative work. [11:32]

Using line integrals to find the work done on a particle moving through a vector field.

A thorough explanation of line integration and how to represent force fields, include graphs and diagrams for visual reference and examples.

Showing that the line integral along closed curves of conservative vector fields is zero.

This resource explains line integrals in relation to conservative vector fields. It contains example problems with solutions and additional problems to work.

This video shows how to plot fractions, negative numbers, decimals, and fractions on a number line. Practice problems are available. [1:58]

Provided are links to Khan Academy content on the following subjects: Computers and the Internet; HTML/CSS; Cryptography; and SOPA/PIPA.