Line integral

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

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

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

I know [itex]\int_C Pdx+Qdy[/itex] 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.

[tex]M =\int_C \delta(s)\,ds[/tex]
 

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