StellarIn Unit 6, calculus shifts from rates of change to accumulation. If derivatives tell you how fast a quantity is changing at an instant, then integrals tell you the total effect of that change over an interval. The basic idea is that if a rate function is known, then the total amount gained or lost can be found by adding up many small changes. For example, if water flows into a tank at a variable rate, then the total amount of water added over a time interval is the accumulation of that rate. This is the start of integral thinking: instead of looking at one instant, you look at how many tiny pieces of change combine into one total amount.
Accumulation connects naturally to area. If a rate function is graphed, then the accumulation over an interval can often be interpreted as the signed area between the graph and the x-axis. Positive regions contribute positively, and negative regions contribute negatively. This is why integration is closely tied to both geometry and change. You should understand that accumulation is not just “adding numbers,” but adding infinitely many tiny contributions in a structured way. This idea becomes the foundation for Riemann sums, definite integrals, and the Fundamental Theorem of Calculus later in the unit.