Improper Integrals
Evaluation of improper integrals with infinite limits or infinite discontinuities. Students will determine the convergence or divergence of these integrals.
About This Topic
Evaluation of improper integrals with infinite limits or infinite discontinuities. Students will determine the convergence or divergence of these integrals.
Key Questions
- What distinguishes an improper integral from a standard definite integral?
- How do we use limits to evaluate improper integrals?
- What does it mean geometrically for an improper integral to converge?
Planning templates for Further Mathematics
5E Model
The 5E Model structures lessons through five phases (Engage, Explore, Explain, Elaborate, and Evaluate), guiding students from curiosity to deep understanding through inquiry-based learning.
Unit PlannerMath Unit
Plan a multi-week math unit with conceptual coherence: from building number sense and procedural fluency to applying skills in context and developing mathematical reasoning across a connected sequence of lessons.
RubricMath Rubric
Build a math rubric that assesses problem-solving, mathematical reasoning, and communication alongside procedural accuracy, giving students feedback on how they think, not just whether they got the right answer.
More in Advanced Calculus
Reduction Formulae
Derivation and application of reduction formulae for the integration of functions raised to a power. Students will use integration by parts to establish recursive relationships.
2 methodologies
Arc Length and Surface Area of Revolution
Calculation of the arc length of curves and the surface area of solids generated by revolution. Students will apply definite integrals to Cartesian and parametric equations.
2 methodologies