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O-LevelAdditional MathematicsDifferentiation and integration4037/11 · Oct/Nov 2011 · Q811 Marks

Find ∫ (eˣ + 1)² dx and hence evaluate ∫₂⁰ (eˣ + 1)² dx.

  1. (a)Find ∫ (eˣ + 1)² dx and hence evaluate ∫₂⁰ (eˣ + 1)² dx.[6]
  2. (b)A curve is such that dy/dx = (4x+1)⁻¹/². Given that the curve passes through the point with coordinates (2, 4.5), find the equation of the curve.[5]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2011). The mark or mark type is shown in brackets.

  1. [1] (a) M1 for expansion ∫ e^(2x) + 2e^x + 1 dx
  2. [1] (a) B1 for e^(2x)/2
  3. [1] (a) B1 for 2e^x
  4. [1] (a) B1 for +x
  5. [2] (a) M1 for correct use of limits [e^(2x)/2 + 2e^x + x] from 0 to 2 = 41.6
  6. [1] (b) M1 for attempt to integrate y = (4x+1)^(1/2) / 2 (+c)
  7. [1] (b) A1 for (4x+1)^(1/2)
  8. [1] (b) A1 for 1/2 (4x+1)^(1/2)
  9. [1] (b) M1 for attempt to find c, must be from integration, when y = 4.5, x = 2, c = 3
  10. [1] (b) A1 for c = 3

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About this question

Topic
Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 11 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2011 Paper 1 Variant 1, question 8.

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