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A-LevelMathematicsIntegration9709/21 · Oct/Nov 2019 · Q25 Marks

Find the exact value of ∫₀¹ (2e^(2x) – 1)² dx. Show all necessary working.

  1. (a)Find the exact value of ∫₀¹ (2e^(2x) – 1)² dx. Show all necessary working.[5]

Mark scheme

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

  1. [B1] Expand integrand to obtain 4e^(4x) – 4e^(2x) +1
  2. [*M1] Integrate to obtain at least two terms of form k₁e^(4x) + k₂e^(2x) + k₃x
  3. [A1] Obtain correct e^(4x) - 2e^(2x) + x
  4. [DM1] Apply both limits correctly to their integral
  5. [A1] Obtain e⁸-3e⁴ + 2e² +1

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About this question

Topic
Integration, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, Oct/Nov 2019 Paper 2 Variant 1, question 2.

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