A-level · Integration

Integrating with trigonometric identitiesExam-style questions

Integrating trig functions that have no table entry by rewriting them first. Why sin²x is not ⅓sin³x; the cos 2x identities for squares of sine and cosine; exact values over an interval; tan² and cot² through the Pythagorean identities; products of sine and cosine through sin 2x; and squares of a multiple angle or a bracket.

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17 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAllLevel 2Level 3Level 5
  1. 1
    Find ∫sin⁡2x dx\displaystyle\int \sin^2 x\,dx.
    Level 2 · 2 marksTry it
  2. 2
    Find ∫cos⁡2x dx\displaystyle\int \cos^2 x\,dx.
    Level 2 · 2 marksTry it
  3. 3
    Find ∫tan⁡2x dx\displaystyle\int \tan^2 x\,dx.
    Level 3 · 2 marksTry it
  4. 4
    Find ∫sin⁡xcos⁡x dx\displaystyle\int \sin x\cos x\,dx.
    Level 3 · 2 marksTry it
  5. 5
    Evaluate ∫0π/2sin⁡2x dx\displaystyle\int_0^{\pi/2} \sin^2 x\,dx.
    Level 3 · 3 marksTry it

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