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6 marksIntegration I

CAPE Pure Mathematics Unit 1 · May/June 2018 · Paper 2 · Question 5(a)

This section contains questions on Algebra, Geometry, and Calculus.

Use the substitution u = x² + 2 to determine ∫(x² + 2)³ (4x³) dx.

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Other parts of this question

  1. 5(b)Calculate the area of the region lying between the parabolas y = x² and x = (1/8)y².[6 marks]
  2. 5(c)(i)Determine f'.[1 mark]
  3. 5(c)(ii)Determine f''.[1 mark]
  4. 5(c)(iii)Calculate the x coordinates of the stationary points of f(x) = 3x⁴ - 2x³ - 6x² + 6x and determine the nature of these stationary points.[11 marks]

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