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A-LevelMathematicsIntegration9709/32 · Feb/Mar 2019 · Q45 Marks

Show that ∫₁⁴ x^(-1/2) ln x dx = 2 – ln 4.

Mark scheme

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

  1. [M1*] Integrate by parts and reach ax^(-1/2)lnx + b∫ x^(-1/2).1/x dx
  2. [A1] Obtain -2x^(-1/2)lnx + 2∫ x^(-3/2) dx, or equivalent
  3. [A1] Complete the integration, obtaining -2x^(-1/2)lnx - 4x^(-1/2), or equivalent
  4. [M1(dep*)] Substitute limits correctly, having integrated twice
  5. [A1] Obtain the given answer following full and correct working

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About this question

Topic
Integration, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, Feb/Mar 2019 Paper 3 Variant 2, question 4.

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