What is the meaning of a triple integral?

[Nathew]

Okay so I just have a question on triple integrals. I understand how to use triple integrals to find volumes, but what I really don't understand is what I am really getting when I take the triple integral OF a function.

I understand physical examples like taking the triple integral of a charge/mass density function will give you the total charge/mass, but what about when it is not that case?

If someone could clear this up for me that would be great!

Thanks!

 

[homeomorphic]

Well, you could interpret it as a higher-dimensional volume (4-d volume under the graph in 4-d space).

I don't see any issue with always pretending that it's a charge/mass density, unless there is some other interpretation suggested by whatever else you are applying it to.