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2 marksIntegration I

CAPE Pure Mathematics Unit 1 · May/June 2006 · Paper 1 · Question 15(a)

Use the result int_0^a f(x) dx = int_0^a f(a - x) dx, a > 0.

Show that int_0^pi x sin x dx = int_0^pi (pi - x) sin x dx.

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Other parts of this question

  1. 15(b)(i)Hence, show that int_0^pi x sin x dx = pi int_0^pi sin x dx - int_0^pi x sin x dx.[2 marks]
  2. 15(b)(ii)Hence, show that int_0^pi x sin x dx = pi.[5 marks]

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