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5 marksIntegration I

CAPE Pure Mathematics Unit 1 · May/June 2002 · Paper 2 · Question 5(b)(v)

The equation of a curve is given by f(x) = x(x + 2)².

Find the area bounded by the curve and the interval of the x-axis, -2 < x < 0.

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Other parts of this question

  1. 5(a)By expressing x - 4 as (√x + 2)(√x - 2), find lim (x→4) (√x - 2) / (x - 4). Hence, find lim (x→4) (√x - 2) / (x² - 5x + 4).[5 marks]
  2. 5(b)(i)Obtain an expression for f'(x).[3 marks]
  3. 5(b)(ii)Find the stationary point(s) of f.[2 marks]
  4. 5(b)(iii)Determine the nature of the stationary point(s) of f.[5 marks]
  5. 5(b)(iv)Sketch the curve.[5 marks]

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