# Lecture 20: Path independence and conservative fields

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Lesson Summary:

In Lecture 20, we learn about path independence and conservative fields. The fundamental theorem of calculus for line integrals tells us that if we integrate a vector field that's a gradient along a curve, we'll get the value of the potential function at the endpoints. This means that we can avoid computing line integrals by finding a function whose gradient is the given vector field. We also see an example where we use the potential function to easily find the work done by a vector field along a curve, without having to compute line integrals.

Lesson Description:

Learn about path independence and conservative fields, what they mean 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.