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[tex]\int_C f(x,y,z)ds[/tex]

might be the total mass of a wire where f describes the linear density of the wire.

But can anybody give an example of a physical or geometric interpretation of the line integral with respect to x (or y, or z)?

i.e. given some specific function f(x,y,z) and points A and B on that curve I can calculate

[tex]\int_C f(x,y,z)dx[/tex]

from A to B to answer an exercise in the textbook.

But what would it mean?