# Lecture 19: Vector fields and line integrals in the plane

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Lesson Summary:

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.

Lesson Description:

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.