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This topic integrates trigonometric functions — sin, cos, sec² and forms needing identities such as the double angle formulae to rewrite sin²x or cos²x before integrating. It's a key topic in A-Level and International A-Level (iAL) Pure Mathematics. This free interactive eClassroom course walks through each step with worked examples and instant-feedback questions, so you can practise until it's secure.
How you do it
Use an identity to rewrite the integral in a form you can integrate. Even powers of sine and cosine need the double angle formulae; odd powers need one factor split off and a substitution. Products of different angles use the sum-to-product identities.
Before you start
This builds directly on trigonometric identities and standard integrals. It sets up areas and volumes involving trigonometry.
What you learn
Many trig expressions are not standard integrals — you must rewrite them with an identity first. The course works through squares via double-angle, combining identities and definite integrals & area. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
Integration of Trig Functions is a Integration topic in the A-level syllabus, covered here at the second year of A-level. The course is built from 5 concept sections, 5 worked examples and 5 check points before the exam-style set. It sits alongside Integration of xⁿ, Integration Using Partial Fractions, Reverse Chain Rule, Trapezium Rule and Volumes of Revolution in the same strand. Endless extra practice on this strand is available on the Integration revision engine, which generates a fresh question each time.
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