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One can integrate the equation for the volume of a sphere, but does it have any real world meaning? When I think of integration, I think of "Area under the curve integrated". But what does the integration of the eq for volume mean? Density? Or nothing at all. Is there a branch of investigation concerning the meanings of derivation and integration because it's pretty interesting to try to understand it in terms of physical meanings.

I know that there is meaning for the rate of change of velocity and so on but it's not readily intuitive to most. So maybe there's a meaning to the area under the curve 4/3 pi R ^3.

That equation can be plotted so there must be an area under it above the x axis. So what does this area imply?

I've search hi and lo on the net and have never seen any discussion on this. If one can develop an intuitive sense of calculus, it would be an easier topic to take on.

Thx,

Rocky