Instructional priorities
- Improper integrals
- Infinite intervals
- Unbounded integrands
- p-integrals
- Comparison
- Trapezoidal rule
- Midpoint rule
- Simpson’s rule
- Error analysis
Faculty planning and evidence
Improper Integrals & Numerical Integration
How do limits, comparison, numerical methods, and error bounds extend integration beyond elementary antiderivatives and finite intervals?
Evidence expectations
Require method selection, exact notation, conditions, units, interpretation, and an independent verification. Score the reasoning chain, not only the final value.
Common interventions
Use retrieval diagnostics, smaller algebraic cases, multiple representations, worked-example fading, error comparison, and oral explanation before assigning more repetition.
Assessment sequence
Formative checks → pathway set → investigation → mastery check → correction → reassessment. Preserve both first-attempt and corrected evidence.