Net Change Theorem

The Net Change Theorem is a fundamental principle in calculus that establishes a direct relationship between a function’s rate of change and its accumulated change over an interval. Mathematically, it states that the definite integral of a function's derivative over a given interval [a,b] yields the net change in the original function:

The Net Change Theorem is an interpretation of the Fundamental Theorem of Calculus. It states that when a rate function is integrated over an interval, it gives the net change in the original quantity.

This applies to real systems like reservoir management. Here, the net rate of volume change includes inflow from a river and outflow throug...