Consider now the problem of finding the work $W$ done by a force $\FF$ in moving a particle along a curve $C$. We begin with the relationship \begin{equation} \hbox{work} = \hbox{force} \times \hbox{distance} \end{equation} Suppose you take a small step $d\rr$ along the curve. How much work was done? Since only the component along the curve matters, we need to take the dot product of $\FF$ with $d\rr$. Adding this up along the curve yields \begin{equation} W = \Lint \FF\cdot d\rr \end{equation}

So how do you evaluate such an integral?

Use what you know!