17–20% of the AP exam. Key topics: Riemann sums (LRAM, RRAM, Midpoint, Trapezoidal), Definite integrals as limits of Riemann sums, Fundamental Theorem of Calculus Part 1, Fundamental Theorem of Calculus Part 2, u-substitution for indefinite and definite integrals, Accumulation functions and their derivatives, Properties of definite integrals.
Unit 6 is the conceptual bridge between Units 2–3 (differentiation) and the rest of calculus. The Fundamental Theorem of Calculus (FTC) is the reason differentiation and integration are inverse operations — and it appears in some form on nearly every AP Calculus exam.
**FTC Part 1** tells you how to differentiate an accumulation function. **FTC Part 2** tells you how to evaluate a definite integral using an antiderivative. Know which part applies before writing anything.
On the AB exam, Unit 6 carries 17–20% of the exam weight — the highest of any unit. FTC Part 1 with a composite upper bound (requiring the chain rule) appears in almost every exam year, often as a no-calculator FRQ part. Riemann sums (trapezoidal approximation) appear frequently in FRQs involving tabular data.
**Most common FTC Part 1 error:** When the upper bound is $u(x)$ rather than just $x$, students evaluate $f(u(x))$ correctly but omit the factor $u'(x)$. This loses a rubric point every time. Write the chain rule factor explicitly, even if it equals 1.
Free-response questions from past AP exams that test this unit's concepts.
