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Confused. :shy:

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Confused. :shy:

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You sound like you might be asking what the physical interpretations of these various line integrals are. The last one, G(x,y)ds, is called

Confused. :shy:

There isn't any obvious physical description of the line integrals of G(x,y) with respect to x or y (not one that I can think of, anyway). But I can say this much. The differential dx represents a change from (x,y) to a new point, in the x direction, and dy represents an analogous small change in the y direction. The differential ds represents a change beginning at some point (x,y) and ending at another point,

Computationally, these line integrals are very simple. If curve C can be parametrized according to two functions x(t) and y(t), then just rewrite the integrands like this:

[tex]G(x(t),y(t))\frac{dx}{dt}dt[/tex]

[tex]G(x(t),y(t))\frac{dy}{dt}dt[/tex]

[tex]G(x(t),y(t))\sqrt{(\dfrac{dx}{dt})^{2}+(\frac{dy}{dt})^{2}}[/tex]

And that's how you do line integrals.

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