Integration techniques and applications.
Choose and justify integration techniques, then calculate exact accumulations, areas and volumes with correct domains and units.
Work through the topic
Learn the method, follow the examples, then try the worksheet.
- 01
Further antiderivatives
Extend antiderivative rules and use initial values to select the correct member of a family.
- 02
Inverse-trigonometric derivatives and integrals
Recognise inverse-trigonometric antiderivatives and account for scaling and real domains.
- 03
Substitution
Choose substitutions that turn a composite integrand into a simpler variable, including definite integrals.
- 04
Trigonometric identities in integration
Rewrite trigonometric integrands using identities before integrating.
- 05
Simple partial fractions
Decompose rational expressions into simple fractions and integrate with correct domain restrictions.
- 06
Integration by parts
Use integration by parts for products and repeat it when needed.
- 07
Selecting/combining methods
Choose and combine techniques based on structure rather than surface appearance.
- 08
Definite integration
Evaluate definite integrals with valid limits, domains and sign checks.
- 09
Areas
Calculate geometric area by identifying boundaries, intersections and the upper curve on each interval.
- 10
Volumes of revolution about either coordinate axis
Use disk and washer cross-sections to calculate volumes around either coordinate axis.
- 11
Interpreting a result in context
Translate integrals into accumulated quantities, average values and meaningful physical units.
Topic review
Revisit the key ideas, then choose a practice paper.