Recovering Totals from Marginal Quantities

In economics, a marginal quantity is a derivative. Marginal cost $C'(q)$ measures the approximate change in total cost for one additional unit near production level $q$. Integrating a marginal function over a production interval recovers the net change in the corresponding total function. One known total value is then needed to recover the absolute total.

The interpretation should not be reduced to symbol manipulation. The integral $\int_a^b C'(q)\,dq$ is the increase in cost from producing $a$ units to producing $b$ units, not the total cost at $b$ unless $C(a)=0$. Units provide the distinction: dollars per unit times units gives dollars. The same reasoning applies to marginal revenue, marginal profit, and other accumulated business quantities.