Unit route
Study lessons in order, complete the pathway selected by diagnostic evidence, conduct the investigation, then demonstrate mastery. Reassessment follows correction and reflection.
Weeks 28, 29, 30 · 7 detailed lessons
Fundamental Theorem & Antiderivatives
How does the Fundamental Theorem connect instantaneous rate with accumulated change?
Pathways
Lesson 01 · Week 28
The Fundamental Theorem of Calculus, Part I
The Fundamental Theorem of Calculus connects accumulation and instantaneous rate. Differentiating an accumulation function recovers the integrand, while evaluating an antiderivative computes…
Lesson 02 · Week 28Accumulation Functions and Variable Bounds
The Fundamental Theorem of Calculus connects accumulation and instantaneous rate. Differentiating an accumulation function recovers the integrand, while evaluating an antiderivative computes…
Lesson 03 · Week 28The Fundamental Theorem of Calculus, Part II
The Fundamental Theorem of Calculus connects accumulation and instantaneous rate. Differentiating an accumulation function recovers the integrand, while evaluating an antiderivative computes…
Lesson 04 · Week 29Antiderivatives and Indefinite Integrals
An antiderivative reverses differentiation. Indefinite integrals represent families of functions and therefore require a constant of integration; initial conditions select one member.…
Lesson 05 · Week 29Initial Conditions and Particular Solutions
An antiderivative reverses differentiation. Indefinite integrals represent families of functions and therefore require a constant of integration; initial conditions select one member.…
Lesson 06 · Week 30Basic u-Substitution
Substitution reverses the chain rule. A successful substitution matches an inner expression with its derivative factor and transforms limits when working with a definite integral.…
Lesson 07 · Week 30Definite Integrals with Substitution
Substitution reverses the chain rule. A successful substitution matches an inner expression with its derivative factor and transforms limits when working with a definite integral.…