Trapezium Rule

This numerical method allows for the approximation of definite integrals. Learners will understand its derivation, apply it to estimate areas under curves, and analyse its accuracy and practical use where exact integration is difficult.

Learning Outcomes:
The learner should be able to:

• Derive the formula for the trapezium rule.
• Use the trapezium rule to estimate definite integrals and areas under curves.
• Determine and compare the exact area under a given curve with the trapezoidal solutions.
• Use the trapezium rule to approximate definite integrals.
• Compare exact and estimated values to assess accuracy.
• Analyse the errors in the trapezium rule in relation to different step sizes.
• Apply the rule in real-world scenarios such as distance or area estimation.
• Generate a comparison between numerical and analytical solutions to integral problems.