So I understand the meaning of an integral of a function, which is the area of the region under the curve that represents that function within the limits of integration.

I also understand the meaning of which is the area of the region D and which is the volume of a solid V.

What I don't understand, even though I do it all the time, is the meaning of a double integral (and a triple integral) of a function. For example: and .

Thanks in advance.