Integration of Trigonometric Functions

Find indefinite integrals of single trig terms such as sin(ax) and cos(ax) using standard antiderivative rules.

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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-ALG-ER-K-Y9-04

Resources

Terminology

  • Antiderivative
  • Indefinite integral
  • Definite integral
  • Constant of integration
  • sec^2(x)
  • Standard antiderivative rule

Task goals

  • Foundation: Find indefinite integrals of single trig terms such as sin(ax) and cos(ax) using standard antiderivative rules.
  • Proficient: Integrate sums and scalar multiples of trig functions, including sec^2(x), and evaluate definite integrals over a given interval.
  • Excellence: Apply integration of trig functions within multi-step NCEA-style problems, such as area-under-a-curve or motion contexts requiring simplification with trig identities first.

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