Techniques of Integration and Differential Equations

Lesson 6.1 · AP 7.1–7.4; Euler method: BC 7.5

Differential equations, slope fields, and Euler’s method

Interpret a differential equation as local slope information, verify solutions, and approximate a solution through successive tangent steps.

Reading reference: Larson & Edwards §6.1

Lesson 6.2 · AP 7.6–7.8; logistic: BC 7.9

Separation of variables, growth, and logistic models

Solve separable initial-value problems, preserve equilibrium solutions, and interpret exponential or logistic behavior.

Reading reference: Larson & Edwards §§6.2–6.3

Lesson 6.3 · BC extensions: AP 6.11–6.12

BC extension · Optional for AP Calculus AB

Integration by parts and partial fractions

Choose between reversing the product rule and decomposing a rational function, then verify the resulting antiderivative.

Reading reference: Larson & Edwards §§8.2, 8.5

Lesson 6.4 · BC extension: AP 6.13

BC extension · Optional for AP Calculus AB

Improper integrals and convergence

Replace infinite bounds and singular endpoints with limits, test convergence, and reject cancellation across a divergent singularity.

Reading reference: Larson & Edwards §8.8