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5 marksIntegration I

CAPE Pure Mathematics Unit 1 · May/June 2014 · Paper 2 · Question 6(b)(i)

The equation of a curve is given by f(x) = 2x√(1 + x²).

Evaluate ∫₀³ f(x) dx.

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Other parts of this question

  1. 6(a)(i)a)Find the equation of the curve[4 marks]
  2. 6(a)(i)b)Find the coordinates of the stationary points and determine their nature.[8 marks]
  3. 6(a)(ii)Sketch the curve in (a) (i) a) above, clearly marking ALL stationary points and intercepts.[4 marks]
  4. 6(b)(ii)Find the volume generated by rotating the area bounded by the curve in (b) (i) above, the x-axis, and the lines x = 0 and x = 2 about the x-axis.[4 marks]

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