2 min read•february 20, 2021

..This unit marks a departure from the path AP Calc has taken thus far. Think about it, to this point, you’ve found the __slope of the line tangent__ to a curve at a point; you’ve __calculated velocity__ when given a position function; you’ve determined __function maxima__. In other words, you’ve investigated rates of change, rates of change, and some more __rates of change__.

Well, we’ve seen how to analyze the instantaneous rate of change of a curve—say one that measures bacteria population as a function of time; but suppose that we know the **rate function**—or how the population changes as a function of time. Can this tell us how much the population it measures changes during a specific time interval?

Have you heard the saying the more things *change *the more things stay the same?

It’s true here, as well—with a twist. The difference is that through **differentiation** we’re measuring *rates* of change, while **integration**—our new process—measures *net* change.

While integration is a concept and process distinct from differentiation, these ideas are linked. In fact, their underlying connection unifies the branches of *differential *and *integral* calculus. But we’ll talk about the __Fundamental Theorem of Calculus__ a bit later on.

For now, takeaway **#1** should be that integration helps to measure the **net change** given a rate function. And takeaway **#2**? Well, this is a fairly important topic—and the College Board® thinks so, too—because whether you sit the AB or BC exam, integration carries a 17-20% weighting!

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