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A-LevelMathematicsNumerical methods9709/22 · Feb/Mar 2018 · Q35 Marks

Use the trapezium rule with four intervals to find an approximation to ∫₀⁸ ln(x + 2) dx, giving your answer correct to 3 significant figures.

  1. (i)Use the trapezium rule with four intervals to find an approximation to ∫₀⁸ ln(x + 2) dx, giving your answer correct to 3 significant figures.[3]
  2. (ii)Hence find an approximation to ∫₀⁸ 3 ln(x² + 4x + 4) dx.[2]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2018). The mark or mark type is shown in brackets.

  1. [B1] Use y-values ln 2, ln 4, ln 6, ln 8, ln 10 Or decimal equivalents
  2. [M1] Use correct formula, or equivalent, with h = 2 and five y-values
  3. [A1] Obtain 13.5
  4. [B1] Recognise integrand as 6ln(x + 2)
  5. [B1] Obtain 81 or 81.0 or 81.1

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About this question

Topic
Numerical methods, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, Feb/Mar 2018 Paper 2 Variant 2, question 3.

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