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 25, 26, 27 · 7 detailed lessons
Accumulation, Riemann Sums & Definite Integrals
How can infinitely refined sums measure net change and accumulated quantity?
Pathways
Lesson 01 · Week 25
Accumulation and Area as a Limit
A definite integral measures signed accumulation. The integrand gives a rate or density, the differential gives the input unit, and their product determines the accumulated unit.…
Lesson 02 · Week 25Left and Right Riemann Sums
Riemann sums approximate accumulation by adding height-times-width contributions. The sample-point rule and partition determine the estimate; refinement generally improves resolution.…
Lesson 03 · Week 25Midpoint Sums
Riemann sums approximate accumulation by adding height-times-width contributions. The sample-point rule and partition determine the estimate; refinement generally improves resolution.…
Lesson 04 · Week 26Trapezoidal Approximation
Riemann sums approximate accumulation by adding height-times-width contributions. The sample-point rule and partition determine the estimate; refinement generally improves resolution.…
Lesson 05 · Week 26Definite Integral Notation and Signed Area
A definite integral measures signed accumulation. The integrand gives a rate or density, the differential gives the input unit, and their product determines the accumulated unit.…
Lesson 06 · Week 27Properties of Definite Integrals
A definite integral measures signed accumulation. The integrand gives a rate or density, the differential gives the input unit, and their product determines the accumulated unit.…
Lesson 07 · Week 27Net Change and Units of Accumulation
A definite integral measures signed accumulation. The integrand gives a rate or density, the differential gives the input unit, and their product determines the accumulated unit.…