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5 marksIntegration I

CAPE Pure Mathematics Unit 1 · May/June 2017 · Paper 2 · Question 6(c)

Given that ∫[-1,3] (3f(x) + g(x)) dx = 5 and ∫[-1,3] (5f(x) - 2g(x)) dx = 1, determine ∫[-1,3] f(x) dx and ∫[-1,3] g(x) dx.

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Other parts of this question

  1. 6(a)(i)On the axes below, sketch triangle PQR.[1 mark]
  2. 6(a)(ii)Determine the equations of EACH of the following: PQ, QR, PR.[7 marks]
  3. 6(a)(iii)Hence, use integration to determine the area of triangle PQR.[7 marks]
  4. 6(b)The voltage in a circuit, V, satisfies the equation dV/dt + V/2.5 = 0. Given that V = 25 volts when t = 0 seconds, write an expression for V in terms of t.[5 marks]

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