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4 marksIntegration II

CAPE Pure Mathematics Unit 2 · May/June 2016 · Paper 2 · Question 2(c)(iii)

Let f(x) = (x^2 + 2x + 3) / ((x - 1)(x^2 + 1)) for 2 <= x <= 5.

Hence, determine the value of the integral from 2 to 5 of f(x) dx.

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Other parts of this question

  1. 2(a)Determine partial derivative of w with respect to x.[4 marks]
  2. 2(b)Determine the integral of e^(2x) sin(e^x) dx.[6 marks]
  3. 2(c)(i)Use the trapezium rule with three equal intervals to estimate the area bounded by f and the lines y = 0, x = 2 and x = 5.[5 marks]
  4. 2(c)(ii)Using partial fractions, show that f(x) = 3/(x - 1) - (2x)/(x^2 + 1).[6 marks]

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