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A-LevelMathematicsIntegration9709/21 · May/June 2019 · Q47 Marks

Find ∫ tan² 3x dx.

  1. (a)Find ∫ tan² 3x dx.[3]
  2. (b)Find the exact value of ∫₀¹ (e³ˣ + 4)/eˣ dx. Show all necessary working.[4]

Mark scheme

Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.

  1. [B1] Use identity tan² 3x = sec² 3x−1
  2. [M1] Integrate to obtain form k₁ tan 3x + k₂x
  3. [A1] Obtain correct (1/3) tan 3x - x + c
  4. [B1] Express integrand as e²ˣ + 4e⁻ˣ
  5. [M1] Integrate to obtain form k₃e²ˣ + k₄e⁻ˣ
  6. [A1] Obtain correct (1/2)e²ˣ - 4e⁻ˣ
  7. [A1] Use limits to obtain (1/2)e² - 4e⁻¹ + 3/2 or similarly simplified equivalent

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About this question

Topic
Integration, A-Level Mathematics (syllabus 9709). Structured question, 7 marks.
Source
A-Level Mathematics, May/June 2019 Paper 2 Variant 1, question 4.

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