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O-LevelAdditional MathematicsDifferentiation and integration4037/22 · Oct/Nov 2023 · Q66 Marks

Find the exact value of ∫₂³ ((x+2)² / x) dx.

  1. Find the exact value of ∫₂³ ((x+2)² / x) dx.[6]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.

  1. [B2] B1 for two terms correct for (x+2)² / x = x + 4 + 4/x soi
  2. [B2] B1 for x²/2 + ... + 4lnx for ∫(x + 4 + 4/x) dx = x²/2 + 4x + 4lnx
  3. [M1] dep on at least previous B1 for integration for [x²/2 + 4x + 4lnx]₃²
  4. [A1] 6.5 + 4ln(3/2) or exact equivalent

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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 2023 Paper 2 Variant 2, question 6.

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