Quelpr
4 marksIntegration II

CAPE Pure Mathematics Unit 2 · May/June 2024 · Paper 2 · Question 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.

The mark scheme is shown once you've answered.

Practise this question

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)(i)Derive the reduction formula ∫ sinⁿ x dx = -1/n sinⁿ⁻¹ x cos x + (n-1)/n ∫ sinⁿ⁻² x dx.[6 marks]

More practice: the rest of this paper · more Integration II questions · all CAPE Pure Mathematics Unit 2 past papers