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9 marksIntegration I

CAPE Pure Mathematics Unit 1 · 2021 · Paper 2 · Question 5(b)

A sketch of the curves is shown below.

Calculate the area of the region enclosed by the parabolas y = x² and y = 6x - 3x².

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Other parts of this question

  1. 5(a)Use the substitution u = (x³ + 4) to determine ∫ 3x² (x³ + 4)⁴ dx.[6 marks]
  2. 5(c)(i)Show that f(x) has stationary points at x = -1, x = 0 and x = 2.[6 marks]
  3. 5(c)(ii)Determine the nature of these stationary points.[4 marks]

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