What is the definition of a line integral?

coverband
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How would you DEFINE the line integral:

int_aroundc[P(x,y)dx + Q(x,y)dy]
 
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What's that supposed to mean? Isn't it already defined as you have written it?
 
That what I thought but I think there's some definition with limits and zeta and stuff...
 
You would define such an integral by choosing a parameterization for the path. Then it reduces to a regular integral in terms of the parameter. I don't know what "zeta" has to do with it but all the limits are hidden in the definition of the regular integral.
 

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