Lesson Plan

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Lesson Plan
Grade: Date: 17/01/2026
Subject: Mathematics
Lesson Topic: Integration: techniques, volumes of revolution, differential equations
Learning Objective/s:
  • Apply substitution, integration by parts, partial fractions, trigonometric integrals, and trig‑substitution to evaluate indefinite integrals.
  • Select and execute the appropriate disk, washer, or shell method to find volumes of revolution.
  • Solve separable and linear first‑order differential equations using separation of variables and integrating factors.
  • Determine the general solution of homogeneous second‑order linear ODEs with constant coefficients.
  • Use the method of undetermined coefficients to obtain particular solutions of non‑homogeneous second‑order ODEs.
Materials Needed:
  • Projector and screen
  • Whiteboard and markers
  • Worksheet packets (integration techniques, volume problems, ODE practice)
  • Graphing calculators
  • Ruler/compass for sketching solids of revolution
  • Computer with CAS software for demonstration (optional)
 Introduction:
Begin with a quick visual of a solid generated by rotating a simple region to spark curiosity. Review that students already know basic antiderivatives and the product rule. State that by the end of the lesson they will be able to choose the right technique for any integral, compute volumes, and solve common differential equations.
Lesson Structure:
  1. Do‑Now (5'): Short quiz on basic antiderivatives to activate prior knowledge.
  2. Mini‑lecture (10'): Overview of the five integration techniques with one concise example each.
  3. Guided practice (15'): Students work in pairs on a mixed‑technique worksheet; teacher circulates, prompting the LIATE rule for integration by parts.
  4. Volume methods (10'): Demonstrate disk, washer, and shell formulas on the board; students sketch a region and identify the best method.
  5. ODE introduction (10'): Present separable and linear first‑order equations, then the characteristic‑root method for second‑order ODEs.
  6. Exit ticket (5'): Two quick problems – one integration technique choice, one ODE to solve – to check mastery.
Conclusion:
Recap the decision‑tree for choosing an integration technique and the three volume methods. Collect exit tickets and highlight common errors. Assign homework: a set of integrals covering all techniques, two volume‑of‑revolution problems, and one non‑homogeneous second‑order ODE to solve using undetermined coefficients.