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3 marksIntegration II

CAPE Pure Mathematics Unit 2 · May/June 2006 · Paper 2 · Question 2(b)(iii)

Given that I_n = int_0^1 x^n e^x dx, where n in N.

Hence, or otherwise, evaluate I_3, writing your answer in terms of e.

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Other parts of this question

  1. 2(a)(i)Express (1 + x)/((x - 1)(x^2 + 1)) in partial fractions.[6 marks]
  2. 2(a)(ii)Hence, find int (1 + x)/((x - 1)(x^2 + 1)) dx.[3 marks]
  3. 2(b)(i)Evaluate I_1.[4 marks]
  4. 2(b)(ii)Show that I_n = e - n I_(n-1).[4 marks]

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