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O-LevelAdditional MathematicsDifferentiation and integration4037/22 · Oct/Nov 2020 · Q66 Marks

Find the exact value of ∫₄² (x+1)² / x² dx.

  1. Find the exact value of ∫₄² (x+1)² / x² dx.[6]

Mark scheme

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

  1. [B1] (x+1)² / x² = (x²+2x+1) / x² = 1 + 2/x + 1/x² for expanding numerator seen anywhere. M1 for attempt to divide their three term numerator by x².
  2. [A2/1/0] ∫[1 + 2/x + 1/x²]dx = x + 2lnx - 1/x (+ c) minus 1 each error or omission.
  3. [M1] [x + 2lnx - 1/x]⁴₂ Dep insert 4 and 2 into their three or two term integrand and subtract correctly.
  4. [A1] = 9/4 + 2ln2 oe must be exact two terms. isw

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About this question

Topic
Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 6 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2020 Paper 2 Variant 2, question 6.

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