Chapter 3 Integrating one-forms: line integrals
We study how one-forms can be integrated along curves, which leads to the definition of (oriented) line integrals (also called “work integrals”). An important result in this section is the Fundamental Theorem of line integrals, which is the natural generalization of the Fundamental Theorem of Calculus to integrals of one-forms along curves in \(\mathbb{R}^2\) and \(\mathbb{R}^3\text{.}\)