# Line integral

yifli
There are line integral with respect to arc length and line integral with respect x/y.

I know $\int_C Pdx+Qdy$ is useful to calculate the work. When do we need the line integral with respect to arc length?

Homework Helper
Gold Member
There are line integral with respect to arc length and line integral with respect x/y.

I know $\int_C Pdx+Qdy$ is useful to calculate the work. When do we need the line integral with respect to arc length?

Suppose you have a wire with a density which varies along its length. You need an arc length type integral to evaluate its mass.

$$M =\int_C \delta(s)\,ds$$