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A-LevelMathematicsIntegration9709/22 · May/June 2021 · Q48 Marks

Find the exact value of ∫₀² 6e²ˣ⁺¹ dx.

  1. (a)Find the exact value of ∫₀² 6e²ˣ⁺¹ dx.[3]
  2. (b)Find ∫ (tan²x + 4 sin² 2x) dx.[5]

Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

  1. [M1] Integrate to obtain form ke²ˣ⁺¹
  2. [A1] Obtain correct 3e²ˣ⁺¹
  3. [A1] Apply limits correctly to obtain 3e⁵ - 3e
  4. [B1] State tan²x = sec²x - 1
  5. [M1] Express 4sin²2x in the form k₁ + k₂cos4x
  6. [A1] Obtain correct 2 - 2cos 4x
  7. [M1] Integrate to obtain form k₃tan x + k₄x + k₅sin 4x
  8. [A1] Obtain correct tan x + x - (1/2)sin 4x

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About this question

Topic
Integration, A-Level Mathematics (syllabus 9709). Structured question, 8 marks.
Source
A-Level Mathematics, May/June 2021 Paper 2 Variant 2, question 4.

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