Lesson Plan

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Lesson Plan
Grade: Date: 17/01/2026
Subject: Additional Mathematics
Lesson Topic: Evaluate definite integrals and apply integration to find plane areas between curves and lines
Learning Objective/s:
  • Apply the Fundamental Theorem of Calculus to evaluate definite integrals.
  • Determine limits of integration by finding intersection points of curves.
  • Set up and compute integrals for the area between two curves or between a curve and the x‑axis.
  • Interpret the sign of a definite integral and convert it to a geometric area.
  • Check solutions for common errors such as sign mistakes and incorrect limits.
Materials Needed:
  • Projector or interactive whiteboard
  • Printed worksheet with practice integrals and area problems
  • Graph paper and rulers
  • Scientific calculators (or calculator app)
  • Coloured markers for sketching curves
  • Answer key for teacher
 Introduction:
Begin with a quick visual of a shaded region under a curve projected on the screen to spark curiosity. Review the concept of antiderivatives and the Fundamental Theorem of Calculus that students have learned previously. Explain that today they will use these ideas to evaluate definite integrals and to find the area between curves, with success measured by correctly setting up and solving at least two problems.
Lesson Structure:
  1. Do‑now (5’) – Students complete a short worksheet evaluating a simple definite integral using the FTC.
  2. Mini‑lecture (10’) – Recap the FTC, show how to find antiderivatives, and demonstrate the step‑by‑step procedure for definite integrals.
  3. Guided practice (12’) – Work through Example 1 together, highlighting limit substitution and sign considerations.
  4. Transition to areas (5’) – Discuss how an integral represents area and introduce the “upper – lower” formula.
  5. Collaborative activity (15’) – In pairs, students locate intersection points for a given pair of curves, decide the top function, set up the integral, and compute the area (similar to Example 2).
  6. Whole‑class check (8’) – Review solutions, address common pitfalls (sign errors, wrong limits).
  7. Independent practice (10’) – Students solve a new problem involving a curve and the x‑axis (like Example 3) and record their answer.
  8. Exit ticket (5’) – Each student writes the steps they used to find an area and one mistake to avoid.
Conclusion:
Summarise how the Fundamental Theorem of Calculus links antiderivatives to signed area and how subtracting the lower function yields geometric area. Ask a few students to share their solution strategies as a quick retrieval check. Collect exit tickets and assign a homework worksheet with three additional area‑between‑curves problems for reinforcement.