In this lesson, we learn about vector fields and line integrals in the plane. A vector field is a vector that varies with x and y, while a line integral is the work done by a force along a trajectory. We learn how to draw vector fields and how to compute the work done by a force using a line integral. The physical significance of the work done by a force is the amount of energy provided by the force to perform a motion, and the total work done along a trajectory is given by an integral of the force along that trajectory.
Learn about vector fields and line integrals, what they mean, what they look like, and how to find them.
Denis Auroux. 18.02 Multivariable Calculus, Fall 2007. (Massachusetts Institute of Technology: MIT OpenCourseWare). http://ocw.mit.edu (Accessed March 21, 2009). License: Creative Commons Attribution-Noncommercial-Share Alike.