This is about functionality introduced in Maple 2022, which however is still not well known: Integral Vector Calculus and parametrization using symbolic (algebraic) vector notation. Four new commands were added to the Physics:-Vectors package, implementing the parametrization of curves, surfaces and volumes, as well as the computation of path, surface and volume vector integrals. Those are integrals where the integrand is a scalar or vector function. The computation is done from any description (algebraic, parametric, vectorial) of the region of integration - a path, surface or volume.
There are three kinds of line or path integrals:

NOTE Jan 1: Updated the worksheet linked below; it runs in Maple 2022.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

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