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4 marksIntegration I

CAPE Pure Mathematics Unit 1 · May/June 2005 · Paper 2 · Question 6(c)(i)

Use the substitution t = a - x to show that ∫₀ᵃ f(x) dx = ∫₀ᵃ f(a-x) dx.

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Other parts of this question

  1. 6(a)Differentiate, with respect to x, (x² + 7)³ + sin 3x.[6 marks]
  2. 6(b)(i)Determine the values of x for which the function has stationary points.[3 marks]
  3. 6(b)(ii)Determine the values of x for which the function is increasing.[2 marks]
  4. 6(b)(iii)Determine the values of x for which the function is decreasing.[2 marks]
  5. 6(c)(ii)If ∫₀⁴ f(x) dx = 12, use the substitution t = x - 1 to evaluate ∫₁⁵ 3f(x-1) dx.[3 marks]

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