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A-LevelMathematicsIntegration9709/32 · Feb/Mar 2020 · Q47 Marks

Find ∫(π/3 to π/6) x sec²x dx. Give your answer in a simplified exact form.

  1. Find ∫(π/3 to π/6) x sec²x dx. Give your answer in a simplified exact form.[7]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2020). The mark or mark type is shown in brackets.

  1. [M1*] Integrate by parts and reach ax tan x + b ∫ tan xdx
  2. [A1] Obtain x tanx - ∫ tan x dx
  3. [M1] Complete the integration, obtaining a term ±lncosx, or equivalent
  4. [A1] Obtain integral x tan x + ln cos x, or equivalent
  5. [DM1] Substitute limits correctly, having integrated twice
  6. [M1] Use a law of logarithms
  7. [A1] Obtain answer (5/18)√3π - 1/2ln3, or exact simplified equivalent

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About this question

Topic
Integration, A-Level Mathematics (syllabus 9709). Structured question, 7 marks.
Source
A-Level Mathematics, Feb/Mar 2020 Paper 3 Variant 2, question 4.

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