Mathematics — Integration

Exam board: AQA  |  Back to subjects

Board-Specific Note

Spec taught as Pure, Mechanics, and Statistics papers.

Learning Objectives

• Integrate polynomials
• Evaluate definite integrals
• Find area under a curve

Key Points

• Increase power by 1 then divide
• ∫axⁿ dx = axⁿ⁺¹/(n+1) + C
• ∫ₐᵇ f(x)dx = F(b)−F(a)

Lesson Plan (50 minutes)

1. Starter (5 min): Recall prior knowledge of integration with quick questions.
2. Teaching (15 min): Work through each of the learning objectives, explaining principles step by step.
3. Key points review (5 min): Revisit the key points together, confirming understanding.
4. Worked example (10 min): Model the example question: Integrate ∫(2x³ - 5x) dx. Solution: x⁴/2 - 5x²/2 + C
5. Practice (10 min): Students attempt the practice questions independently; circulate and support.
6. Plenary (5 min): Review answers and address misconceptions.

Homework

• ∫(4x² + 3x) dx
• Evaluate ∫₀² (x² + 1) dx
• Area under y = x from x=0 to x=3

Assessment

Check practice answers against the model answer; use the built-in practice questions as formative assessment.