I took a look at the line_integrate() function. The Curve class is 
something of a start. Though, I like very much Raoul's idea for a single 
class to represent everything (path/surface/volume). I think this is 
doable. But,

> would then represent an integral over an N-dimensional hypervolume

I have not had a relevant course that would acquaint me with 'N-dimensional 
hypervolumes'. Nevertheless, I am willing to read up on it. I hope that 
just implementing integrals in such hypervolumes wouldn't be too different 
from the 2 or 3 dimensional case.

> How are they numerical in nature? Integrals are by their nature symbolic. 
They take symbolic functions and   > return a symbolic result. Numerics are 
useful if the answer is not expressible in terms of nice functions. 
 
Indeed they are. I said numeric from the user's perspective. For example, 
if a user wants to calculate a line integral, say, then unlike integration 
in one variable where we could do indefinite integrals and expect the 
answer to be in terms of elementary functions, here, we might be just 
concerned with the numeric result of the integration. Of course, giving the 
output in terms of elementary functions would be much better but I am 
inclined to think that we will probably need rely heavily on some kind of a 
numeric backend.


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