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A-LevelFurther MathematicsIntegration9231/12 · Oct/Nov 2019 · Q16 Marks

The curve C has equation y = xº for 0 ≤ x ≤ 1, where a is a positive constant. Find, in terms of a, the coordinates of the centroid of the region enclosed by C, the line x = 1 and the x-axis.

  1. The curve C has equation y = xº for 0 ≤ x ≤ 1, where a is a positive constant. Find, in terms of a, the coordinates of the centroid of the region enclosed by C, the line x = 1 and the x-axis.[6]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

  1. [B1] Finds area of region.
  2. [M1 A1] Finds ∫xy dx.
  3. [M1 A1] Finds ∫(1/2)y² dx.
  4. [A1] Both coordinates correct.

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About this question

Topic
Integration, A-Level Further Mathematics (syllabus 9231). Structured question, 6 marks.
Source
A-Level Further Mathematics, Oct/Nov 2019 Paper 1 Variant 2, question 1.

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