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2 marksIntegration I

CAPE Pure Mathematics Unit 1 · May/June 2011 · Paper 2 · Question 6(b)(ii)a)

Using the result from 6(b)(i).

Show that ∫(from 0 to π) x sin x dx = ∫(from 0 to π) sin x dx - ∫(from 0 to π) x sin x dx

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Other parts of this question

  1. 6(a)(i)Find the coordinates of each of the stationary points A and B[8 marks]
  2. 6(a)(ii)Find the equation of the normal to the curve f(x) = x(x² - 12) at the origin, O[2 marks]
  3. 6(a)(iii)Find the area between the curve and the positive x-axis.[6 marks]
  4. 6(b)(i)Use the result ∫(from 0 to a) f(x) dx = ∫(from 0 to a) f(a-x) dx, where a > 0, to show that ∫(from 0 to π) x sin x dx = ∫(from 0 to π) (π - x) sin x dx.[2 marks]
  5. 6(b)(ii)b)Show that ∫(from 0 to π) x sin x dx = π.[5 marks]

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