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Integrals are of many forms. A simple line integral will give you information about the function of choice.
Surface integrals are a bit more tricky and when the surface is in three dimensions even more so.
This leads to triple integrals where one can play with all of space in three dimensions.
I urge you to look up Maxwells equations for radiation.
Div Grad and Curl are just operators to quantify in three dimensions the values of various derivatives of any complex function.
It gets even trickier when asymtotes are a part of the function.
I have forgotten more than I know now!
Bert
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