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 31, 32 · 7 detailed lessons
Integration Methods & Numerical Analysis
How do structure, approximation, and error analysis guide the evaluation of integrals?
Pathways
Lesson 01 · Week 31
Selecting an Integration Strategy
Integration strategy begins with structure: simplify, split sums, identify reverse derivative patterns, and verify by differentiating the result. Exact and numerical answers should agree wit…
Lesson 02 · Week 31Algebraic Simplification Before Integrating
Integration strategy begins with structure: simplify, split sums, identify reverse derivative patterns, and verify by differentiating the result. Exact and numerical answers should agree wit…
Lesson 03 · Week 31Integrals of Exponential and Logarithmic Forms
Integration strategy begins with structure: simplify, split sums, identify reverse derivative patterns, and verify by differentiating the result. Exact and numerical answers should agree wit…
Lesson 04 · Week 31Integrals of Trigonometric Forms
Integration strategy begins with structure: simplify, split sums, identify reverse derivative patterns, and verify by differentiating the result. Exact and numerical answers should agree wit…
Lesson 05 · Week 32Integration by Parts: Calculus II Bridge
Integration by parts reverses the product rule and serves here as an optional Calculus II bridge. The choice of u should simplify when differentiated, while dv should be easy to integrate.…
Lesson 06 · Week 32Comparing Numerical Integration Methods
Riemann sums approximate accumulation by adding height-times-width contributions. The sample-point rule and partition determine the estimate; refinement generally improves resolution.…
Lesson 07 · Week 32Error, Reasonableness & Technology Verification
Integration strategy begins with structure: simplify, split sums, identify reverse derivative patterns, and verify by differentiating the result. Exact and numerical answers should agree wit…