Section 7.3 Vector Line Integrals
Consider now the problem of finding the work \(W\) done by a force \(\FF\) in moving a particle along a curve \(C\text{.}\) We begin with the relationship
\begin{equation}
\hbox{work} = \hbox{force} \times \hbox{distance} .\tag{7.3.1}
\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 \(d\rr\text{.}\) Adding this up along the curve yields
\begin{equation}
W = \Lint \FF\cdot d\rr .\tag{7.3.2}
\end{equation}
So how do you evaluate such an integral?
Use what you know!