Khan Academy: Calculus: Using Line Integrals to Find Work Done by a Vector Field

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 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 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]

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

Video showing how to find the closed line integral of the dot product of a vector field and a unit normal vector to figure out how fast particles are exiting the region formed by the closed curve. Green's theorem is applied and the...

Video explaining how to use triple integrals to find the mass of a rectangular prism with variable density. [7:26]

Video lesson using the washer method of integration to find the volume of a specific solid of revolution formed by two curves. [8:22]

Video lesson solving a 2010 IIT JEE calculus problem about finding the definite integral of a periodic function. The function in the problem is composed of a cosine function and a greatest integer function. The problem is solved using...

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 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]