Line Integrals      

A line integral is a tool for measuring the interaction between a vector-field and a curve. More to the point, as an object travels through a vector field, it must either work with or work against the vector field.  The accumulation along the path of this instantaneous "working for or against" the vector field is called Work  and is defined by an integral along the path of motion.  Let's explore this idea, after we first load some packages.

>	restart:with(plots):with(plottools):with(VectorCalculus):

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Line Integrals as Pull-Backs

Line Integrals through a Vector Field

Arclength Differentials

Exercises