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A-LevelMathematicsIntegration9709/22 · Oct/Nov 2017 · Q610 Marks

Find the exact value of ∫(from 0 to π/4) sinx(4 sinx + 6 cos x) dx.

  1. (a)Find the exact value of ∫(from 0 to π/4) sinx(4 sinx + 6 cos x) dx.[5]
  2. (b)Given that ∫(from 0 to a) (6 / (3x + 2)) dx = ln 49, find the value of the positive constant a.[5]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

  1. [B1] Obtain 2 - 2cos2x as part of integrand
  2. [B1] Obtain 3 sin 2x as part of integrand
  3. [M1] Integrate to obtain form k₁x + k₂ sin 2x + k₃ cos 2x
  4. [A1] Obtain 2x - sin 2x - ½cos2x or 2x - sin 2x + 3 sin² x
  5. [A1] Apply limits to obtain ½π + ½
  6. [B1] Integrate to obtain 2ln(3x+2)
  7. [*M1] Use at least one relevant logarithm property
  8. [A1] Obtain (3a+2)/2 = 7 or (3a+2)²/4 = 49 or equivalent without ln
  9. [DM1] Solve relevant equation to find a
  10. [A1] Obtain a = 4 only

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About this question

Topic
Integration, A-Level Mathematics (syllabus 9709). Structured question, 10 marks.
Source
A-Level Mathematics, Oct/Nov 2017 Paper 2 Variant 2, question 6.

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