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Can double integrals be interpreted as net change?

Emekadavid

New member
Sep 28, 2020
5
I understand that single integrals over a function can be interpreted as net change. Net change of the quantity between the bounds of the integration. But I am trying hard to understand if double integration can also be regarded as net change? That is, the net change in volume when the two input variables are changing at the same time, or the net change when on variable is held constant and the other variable to the function is changing? I am interpreting it this way because of dA in double integral acting over the function, f(x,y). Am I getting it wrong and can someone clarify me on the intuitive understanding? The textbook I am reading on double integrals does not state it as such but it uses limits of Riemann's sums to prove double integrals as an approximation of the volume so that is why I am trying to see if there is a connection?
thanks