Lesson Plan

• Describe the purpose of integration and its relationship to differentiation.
• Apply basic antiderivative formulas and at least three integration techniques (substitution, integration by parts, partial fractions, trigonometric integrals or substitution).
• Evaluate definite integrals using the Fundamental Theorem of Calculus and compute areas between curves.
• Select and justify the most appropriate technique for a given integrand.

• Projector or interactive whiteboard with prepared slides
• Student worksheets containing practice integrals and area problems
• Graph paper and scientific calculators
• Whiteboard and markers for teacher modelling
• Printed summary handout of integration techniques

Begin with a real‑world example of accumulated distance to highlight why integration matters. Review that students already know how to differentiate basic functions and the concept of antiderivatives. Explain that by the end of the lesson they will be able to choose and execute the correct technique, evaluate definite integrals and find areas between curves.

1. Do‑now (5 minutes): Quick recall of common antiderivative formulas on the board.
2. Mini‑lecture (10 minutes): Present the integration techniques table and key steps.
3. Guided practice (15 minutes): Work through a substitution example and an integration‑by‑parts example, modelling each step.
4. Collaborative activity (15 minutes): Small groups solve a partial‑fractions problem and a trigonometric‑substitution problem; teacher circulates to check understanding.
5. Definite integrals & area (10 minutes): Demonstrate the Fundamental Theorem of Calculus, solve the area‑between‑curves example, and discuss interpretation.
6. Exit ticket (5 minutes): Students write the technique they would use for a new integrand and compute a short definite integral.

Summarise the hierarchy of choosing an integration method and remind students of the FTC for definite integrals and area calculations. Collect exit tickets to gauge immediate understanding. For homework, assign the worksheet with mixed integration problems, including at least two area‑between‑curves tasks.