The Definite Integral and Area Under a Curve
Learn how definite integrals represent accumulated change and area under a curve, with Riemann sums, the Fundamental Theorem of Calculus, and fully worked AP Calculus examples.
Selecting the Correct Integration Technique
Learn how to choose the correct integration technique in AP Calculus AB & BC, including u-substitution, integration by parts, partial fractions, and algebraic simplification.
Riemann Sums: An Introduction
Learn how Riemann sums approximate definite integrals using left, right, and midpoint sums, with step-by-step AP Calculus AB & BC examples.
Riemann Sums Using Unequal Subintervals (Data Tables)
Learn how to use Riemann sums with unequal subintervals and data tables to approximate definite integrals and accumulated change for AP Calculus AB & BC.
Properties of Definite Integrals
Learn the key properties of definite integrals, including reversing limits, splitting intervals, constant multiples, sums and differences, symmetry, and estimating integrals for AP Calculus AB & BC.
Practice Problem Set: u-Substitution
Practice u-substitution with a focused set of AP Calculus AB & BC integration problems, including indefinite integrals, definite integrals, and recognizing reverse chain-rule patterns.
Practice Problem Set: The Fundamental Theorem of Calculus
Practice problems covering both parts of the Fundamental Theorem of Calculus, including accumulation functions, evaluating definite integrals, and differentiating functions defined by integrals.
Practice Problem Set: Riemann Sums and Definite Integrals
Practice Riemann sums and definite integrals with AP Calculus AB & BC problems covering left, right, and midpoint sums, sigma notation, definite integrals, and interpretation.
Numerical Integration from Data Tables
Learn how to approximate definite integrals from data tables using the trapezoidal rule, with step-by-step AP Calculus AB & BC examples and common mistakes.
Mixed Review: Integration Techniques
A mixed review of AP Calculus integration techniques, including u-substitution, integration by parts, trigonometric integrals, and algebraic simplification.