Meet the integral — the second half of calculus. Approximate area with Riemann sums, define the definite integral, use the Fundamental Theorem of Calculus to connect it to antiderivatives, and build a toolkit of antidifferentiation techniques from basic rules to u-substitution and BC methods.
Six ways to master Unit 6 — pick whichever fits how you like to study.
All 14 topics from the College Board CED, in order. Topics 6.11–6.13 are BC only.
Unit 6 introduces integration, the reverse of differentiation and the tool for measuring accumulated change. The area under a rate-of-change curve is the total change, and you approximate it with Riemann sums (left, right, midpoint) and the trapezoidal rule. As the subintervals shrink, these sums approach the definite integral ∫₁₀ f(x) dx, the exact signed area.
The Fundamental Theorem of Calculus ties it all together: the derivative of an accumulation function g(x) = ∫ f(t) dt is f(x), and a definite integral can be evaluated as F(b) − F(a) using any antiderivative F. You’ll learn the basic antiderivative rules, u-substitution (reversing the chain rule), and algebraic setups like long division and completing the square. BC students add integration by parts, partial fractions, and improper integrals, then practice selecting the right technique.
On the exam this unit is 17–20% for both AB and BC — one of the largest — and takes about 18 class periods (AB). The four mathematical practices below run through every topic: