Professor Dave Explains
Stokes's Theorem
Stokes's Theorem is kind of like Green's Theorem, whereby we can evaluate some multiple integral rather than a tricky line integral. This works for some surface integrals too. Let's see how it works!
Khan Academy
Khan Academy: Calculus: Introduction to the Line Integral
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]
Khan Academy
Khan Academy: Calculus: Scalar Field Line Integral Independent of Path Direction
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]
Khan Academy
Khan Academy: Calculus: Using Line Integrals to Find Work Done by a Vector Field
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]
Khan Academy
Khan Academy: Calculus: 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]
Khan Academy
Khan Academy: Calculus: Line Integral Example 2 (Part 2)
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]
Khan Academy
Khan Academy: Calculus: Line Integrals and Vector Fields
Video that first reviews the concept of work, then gives a vector field and sets up a line integral to find the work done on a particle moving along a path using a dot product. [16:46]
Khan Academy
Khan Academy: Calculus: Line Integral Example 1
Video lesson showing how to visualize, set up, and solve a line integral. Integral is solved using u-substitution. [13:02]
Khan Academy
Khan Academy: Calculus: Line Integral Example 2 (Part 1)
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]
Khan Academy
Khan Academy: Using a Line Integral to Find the Work Done by a Vector Field
Using a line integral to find the work done by a vector field example.
Khan Academy
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.
Khan Academy
Khan Academy: Example of Closed Line Integral of Conservative Field
Example of taking a closed line integral of a conservative field
Khan Academy
Khan Academy: Line Integrals for Scalar Functions (Part 2)
An example of finding the surface area along a closed curve using line integrals.
Khan Academy
Khan Academy: Line Integrals for Scalar Functions: Line Integral Example 1
Video lesson showing how to visualize, set up, and solve a line integral.
Khan Academy
Khan Academy: Line Integral Example 2 (Part 1)
Line integral over a closed path (part 1). This video shows 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.
Khan Academy
Khan Academy: Stokes' Theorem: Stokes Example Part 1
This video shows how to apply Stokes theorem to solve a line integral.
Khan Academy
Khan Academy: Stokes' Theorem: Evaluating Line Integral Directly Part 2
Finishing up the line integral with a little trigonometric integration.