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6 marksIntegration II

CAPE Pure Mathematics Unit 2 · May/June 2024 · Paper 2 · Question 2(c)(i)

Derive the reduction formula ∫ sinⁿ x dx = -1/n sinⁿ⁻¹ x cos x + (n-1)/n ∫ sinⁿ⁻² x dx.

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Other parts of this question

  1. 2(a)Determine ∫ e^(2x) sin 3x dx.[8 marks]
  2. 2(b)Use DeMoivre's theorem to show that (1 + 3i)⁴ = 28 - 96i.[7 marks]
  3. 2(c)(ii)Hence, or otherwise, show that ∫ sin⁶ x dx = -1/6 sin⁵ x cos x - 5/24 sin³ x cos x + 5/8 ∫ sin² x dx.[4 marks]

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