The Fundamental Theorem

for

Line Integrals      

The fundamental theorem of calculus is a mathematical triumph, but the power of the fundamental theorem is somewhat muted when only functions of a single variable are considered.  In this section, we see the first multi-variable version of the fundamental theorem, one that applies to line integrals over curves in conservative fields.  Let's explore this idea, after we first load some packages.

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Potentials of Conservative Fields

The Fundamental Theorem and Path Independence

Using the Fundamental Theorem to find Potentials

Exercises