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A-LevelMathematicsIntegration9709/23 · May/June 2025 · Q13 Marks

Show that ∫₂¹¹ (8 / (4x+1)) dx = ln a, where a is an integer to be found.

  1. Show that ∫₂¹¹ (8 / (4x+1)) dx = ln a, where a is an integer to be found.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.

  1. [B1] Integrate to obtain 2ln(4x+1)
  2. [M1] Apply limits correctly to kln(4x + 1) and use at least one relevant logarithm property
  3. [A1] Obtain 2ln45-2ln9=2ln5 or equivalent, and conclude ln 25

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About this question

Topic
Integration, A-Level Mathematics (syllabus 9709). Structured question, 3 marks.
Source
A-Level Mathematics, May/June 2025 Paper 2 Variant 3, question 1.

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