I understand how to evaluate a line integral, but I don't know what it represents geometrically. Say you have [tex]\int_{C} x^4yd\mathbf{s}[/tex]. What does this mean geometrically? I can see that [tex]\int d\mathbf{s}[/tex] is the length of the arc (am I correct?), but I just can't seem to figure out what [tex]\int_{C}f(\mathbf{r}(t))||\mathbf{r}'(t)||dt[/tex] means.
Thanks for your help.
Thanks for your help.