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O-LevelAdditional MathematicsDifferentiation and integration4037/12 · Oct/Nov 2013 · Q56 Marks

Find ∫(9 + sin 3x)dx.

  1. (i)Find ∫(9 + sin 3x)dx.[3]
  2. (ii)Hence show that ∫(from π/9 to π/3) (9 + sin 3x) dx = aπ + b, where a and b are constants to be found.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2013). The mark or mark type is shown in brackets.

  1. [B1] (i) 9x
  2. [B1] -1/3 cos 3x
  3. [B1] Condone omission of + c
  4. [M1] (ii) for correct use of limits in their answer to (i)
  5. [A1] for each term (e.g. 3π + 1/3 and π - 1/6)
  6. [A1] for final answer (2π + 1/2)

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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 2013 Paper 1 Variant 2, question 5.

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