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A-LevelFurther MathematicsIntegration9231/12 · May/June 2017 · Q1214 Marks

Answer only one of the following two alternatives. EITHER The curve C has equation y = ½(eˣ + e⁻ˣ) for 0 ≤ x ≤ 4.

  1. (i)The region R is bounded by C, the x-axis, the y-axis and the line x = 4. Find, in terms of e, the coordinates of the centroid of the region R.[10]
  2. (ii)Show that ds/dx = ½(eˣ + e⁻ˣ), where s denotes the arc length of C, and find the surface area generated when C is rotated through 2π radians about the x-axis.[4]

Mark scheme

Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.

  1. [M1A1]
  2. [M1]
  3. [A1A1]
  4. [M1]
  5. [A1A1]
  6. [M1A1]
  7. [B1]
  8. [M1A1]
  9. [A1]

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About this question

Topic
Integration, A-Level Further Mathematics (syllabus 9231). Structured question, 14 marks.
Source
A-Level Further Mathematics, May/June 2017 Paper 1 Variant 2, question 12.

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