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A-LevelMathematicsIntegration9709/22 · Feb/Mar 2020 · Q36 Marks

It is given that ∫⁽³ᵃ⁾ₐ (2/(2x-5)) dx = ln(7/2). Find the value of the positive constant a.

  1. It is given that ∫⁽³ᵃ⁾ₐ (2/(2x-5)) dx = ln(7/2). Find the value of the positive constant a.[6]

Mark scheme

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

  1. Integrate to obtain kln(2x-5) For non-zero constant k
  2. Apply limits to obtain ln(6a – 5) – ln(2a - 5) = ln 7/2
  3. Apply subtraction law for logarithms OE
  4. Obtain equation (6a-5)/(2a-5) = 7/2 OE without logarithms
  5. Solve equation for a
  6. Obtain a = 25/2

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About this question

Topic
Integration, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source
A-Level Mathematics, Feb/Mar 2020 Paper 2 Variant 2, question 3.

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