Khan Academy: Calculus: Line Integrals and Vector Fields

Video lesson continuing the problem from the previous video on finding the surface area along a closed curve using line integrals. Two line integrals are set up and solved and added to the area found previously. [9:58]

Video lesson showing how to visualize and use line integrals to find the surface area along a closed curved. Problem is solved by using three different line integrals, only one of which is set up and solved in this video. [12:53]

Video lesson showing how to visualize, set up, and solve a line integral. Integral is solved using u-substitution. [13:02]

Video extending the idea of a conservative vector field to show that a closed curve line integral will be equal to zero by showing that the difference of a line integral of a path and a line integral of a path with the same end points...

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]

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 solving a closed line integral by first showing that the vector field is conservative and then knowing based on the information in the previous video that the closed line integral is equal to zero. [11:02]

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]

Video lesson first reviews the definite integral and then introduces the line integral. Shows how to visualize a line integral and set it up. [18:48]

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