Unit route
Complete lessons in sequence, use diagnostic evidence to select a pathway, conduct the investigation, submit corrected work, and demonstrate mastery at 80% or above.
Weeks 12, 13, 14 · 7 college lessons
Improper Integrals & Numerical Integration
How do limits, comparison, numerical methods, and error bounds extend integration beyond elementary antiderivatives and finite intervals?
Pathways
Lesson 01 · Week 12
Infinite-Interval Improper Integrals
Defining infinite bounds through limits.
Lesson 02 · Week 12Unbounded Integrands on Finite Intervals
Splitting at vertical singularities and taking one-sided limits.
Lesson 03 · Week 12Comparison for Improper Integrals
Bounding positive integrands by known convergent or divergent models.
Lesson 04 · Week 13p-Integrals & Threshold Reasoning
Using the exponent threshold for improper power integrals.
Lesson 05 · Week 13Midpoint & Trapezoidal Rules
Approximating signed area from sampled function values.
Lesson 06 · Week 14Simpson’s Rule & Error Structure
Combining quadratic local models and recognizing requirements.
Lesson 07 · Week 14Adaptive Strategy, Nonelementary Integrals & Validation
Selecting truncation and quadrature with reasoned error control.