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A-LevelMathematicsIntegration9709/31 · Oct/Nov 2025 · Q14 Marks

Find the exact value of ∫ from 1 to 2 of ln 3x dx. Give your answer in the form a+lnb, where a and b are integers.

  1. (a)Find the exact value of ∫ from 1 to 2 of ln 3x dx. Give your answer in the form a+lnb, where a and b are integers.[4]

Mark scheme

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

  1. [M1] Commence integration by parts and reach Axln3x + ∫ B/x dx
  2. [A1] Obtain x ln3x – x
  3. [DM1] Substitute limits correctly in an expression of the form Axln3x + Bx
  4. [A1] Obtain -1 + ln12

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About this question

Topic
Integration, A-Level Mathematics (syllabus 9709). Structured question, 4 marks.
Source
A-Level Mathematics, Oct/Nov 2025 Paper 3 Variant 1, question 1.

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