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Confused. :shy:

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- Thread starter LinearAlgebra
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- #1

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Confused. :shy:

- #2

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Confused. :shy:

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

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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