Numerical Integration (Trapezium and Simpson's Rules)

Apply the trapezium rule with a given number of equal-width strips to estimate the area under a simple curve from a table of values.

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Learning objective overview

Master Teaching Guide coverage for this objective.

Current NZC (2007)
  • No direct alignment recorded
New NZC (2026)
  • NZC26-P4-MEA-MEA-P-Y10-03

Resources

Terminology

  • Trapezium rule
  • Simpson's rule
  • Strip width
  • Ordinate
  • Approximation
  • Definite integral

Task goals

  • Foundation: Apply the trapezium rule with a given number of equal-width strips to estimate the area under a simple curve from a table of values.
  • Proficient: Use Simpson's rule with a specified number of strips to estimate a definite integral, and compare trapezium versus Simpson's estimates for the same function.
  • Excellence: Evaluate the accuracy and limitations of numerical integration estimates against the exact integral (where obtainable), and justify strip-number choices or error trends for a given curve shape.

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Numerical Integration (Trapezium and Simpson's Rules)

Numerical Integration (Trapezium and Simpson's Rules)

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