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AP Calc



Unit 6

6.0 Unit 6 Overview: Integration and Accumulation of Change

2 min readfebruary 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.
Oh, yeah, I suppose that’s right. So...what’s next?
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?
Wait, so we’re still studying change?
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.
So differentiation and this integration thing, they’re totally different, then?
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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Unit 10: Infinite Sequences and Series (BC Only)
Unit 1: Limits & Continuity
Unit 2: Differentiation: Definition & Fundamental Properties
Unit 3: Differentiation: Composite, Implicit & Inverse Functions
Unit 4: Contextual Applications of the Differentiation
Unit 5: Analytical Applications of Differentiation
Unit 7: Differential Equations
Unit 8: Applications of Integration
Unit 9: Parametric Equations, Polar Coordinates & Vector Valued Functions (BC Only)
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