Integration and Accumulation of Change Overview — AP Calculus AB
1. Unit at a Glance
We begin by connecting integration to the inverse of differentiation, introducing antiderivatives and basic indefinite integral rules. Next, we build intuition for integration as area under a curve, starting with approximations using Riemann sums before formalizing the definition of the definite integral.
The centerpiece of this unit is the Fundamental Theorem of Calculus (FTC), which unites differentiation and integration, and introduces accumulation functions that describe total change up to any point. We end by learning core integration techniques including u-substitution, and practice selecting the right approach for different integrands.
Common Pitfalls
Why: This common error leads to lost points on both multiple choice and free response AP exam questions
Why: Confusing the FTC for evaluating definite integrals with the FTC for differentiating accumulation functions leads to sign and derivative errors
Why: Leaving the final answer in terms of $u$ results in an incorrect solution, even if intermediate steps are correct