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4 marksIntegration I

CAPE Pure Mathematics Unit 1 · May/June 2010 · Paper 2 · Question 6(b)(ii)

The function f(x) satisfies ∫ from 1 to 4 of f(x) dx = 7.

Using the substitution u = x + 1, evaluate ∫ from 0 to 3 of 2f(x + 1) dx.

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Other parts of this question

  1. 6(a)(i)Differentiate with respect to x: y = sin (3x + 2) + tan 5x.[3 marks]
  2. 6(a)(ii)Differentiate with respect to x: y = (x² + 1) / (x³ - 1).[4 marks]
  3. 6(b)(i)Find ∫ from 1 to 4 of [3 f(x) + 4] dx.[4 marks]
  4. 6(c)(i)Find the coordinates of the points P and Q.[5 marks]
  5. 6(c)(ii)Calculate the area of the shaded portion of the diagram bounded by the curve and the straight line.[5 marks]

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