Lesson 4.1 · AP 6.8; 7.7
Antiderivatives and initial conditions
Reverse differentiation, retain the family of constants, and choose a particular antiderivative from a given condition.
Reading reference: Larson & Edwards §§4.1, 5.2, 5.4
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Unit 4
Integrals and the Fundamental Theorem
The integral arrives twice: as an accumulation built from Riemann sums, and as the reverse of differentiation. The Fundamental Theorem is what joins the two.
Unit 4 practice
12 problems · Questions and worked solutions.
Lessons
Lesson 4.2 · AP 6.1–6.3
Riemann sums, signed area, and numerical integration
Approximate accumulation from graphs and tables, preserve signed contributions, and connect sums to definite integrals.
Reading reference: Larson & Edwards §§4.2–4.3, 4.6
Read lesson →Lesson 4.3 · AP 6.4–6.7
Accumulation functions and the Fundamental Theorem
Connect rates and accumulation, differentiate integrals with variable bounds, and evaluate definite integrals with antiderivatives.
Reading reference: Larson & Edwards §4.4
Read lesson →Lesson 4.4 · AP 6.9–6.10; 6.8
Substitution and inverse-trigonometric integrals
Reverse the chain rule, transform bounds consistently, and recognize standard logarithmic and inverse-trigonometric patterns.
Reading reference: Larson & Edwards §§4.5, 5.2, 5.7
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