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A-LevelMathematicsIntegration9709/33 · May/June 2019 · Q25 Marks

Show that ∫₀^(1/4 π) x² cos 2x dx = (1/8)(π² – 8).

  1. (i)Show that ∫₀^(1/4 π) x² cos 2x dx = (1/8)(π² – 8).[5]

Mark scheme

Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.

  1. [M1*] Commence integration and reach ax² sin 2x + b ∫ x sin 2x dx
  2. [A1] Obtain (1/2)x² sin 2x – ∫ x sin 2x dx, or equivalent
  3. [A1] Complete the integration and obtain (1/2)x² sin 2x + (1/2)x cos 2x – (1/4)sin 2x, or equivalent
  4. [DM1] Use limits correctly, having integrated twice
  5. [A1] Obtain given answer correctly

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About this question

Topic
Integration, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, May/June 2019 Paper 3 Variant 3, question 2.

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