4.3: Stokes' Theorem

Math 4A: Multivariable Calculus · LibreTexts

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    Learning Objectives
    • Explain the meaning of Stokes’ theorem.
    • Use Stokes’ theorem to evaluate a line integral.
    • Use Stokes’ theorem to calculate a surface integral.

    In this section, we study Stokes’ theorem, a higher-dimensional generalization of Green’s theorem. This theorem, like the Fundamental Theorem for Line Integrals and Green’s theorem, is a generalization of the Fundamental Theorem of Calculus to higher dimensions. Stokes’ theorem relates a vector surface integral over a surface \(S\) in space to a line integral around the boundary of \(S\). Therefore, just as the theorems before it, Stokes’ theorem can be used to reduce an integral over a geometric object \(S\) to an integral over the boundary of \(S\).

     

    This page titled 4.3: Stokes' Theorem was last modified on Thu, 04 Dec 2025 11:35:02 GMT and is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Kenn Huber.