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## \sum W = \int (\sum \vec{F}) \cdot d \vec{r} ##

Unfortunately, I haven't the faintest idea how to evaluate this. I know how to evaluate an integral with respect to some parameter, but not with respect to another vector. Help?

(Note: I would be particularly interested to know how to evaluate this if given ##\vec{F}(t)## and ##\vec{r}(t)## ).