- #1
gnome
- 1,041
- 1
I understand that an example of a physical interpretation of the line integral of a scalar function with respect to arc length
[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?
[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?