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 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 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]

Example of taking a closed line integral of a conservative field