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A-LevelFurther MathematicsIntegration9231/12 · Oct/Nov 2019 · Q37 Marks

The integral In, where n is a positive integer, is defined by In = ∫ from 1/2 to 1 of xⁿ sin πx dx.

  1. (i)Show that n(n + 1)In+2 = 2n+1n + π – π²Ιn.[5]
  2. (ii)Find I5 in terms of π and I1.[2]

Mark scheme

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

  1. [M1 A1] Integrates by parts.
  2. [M1] Integrates by parts again.
  3. [M1] Uses I_n.
  4. [A1] AG
  5. [M1] Substitutes I_3 into reduction formula.
  6. [A1] AEF, must be exact with fractions simplified.

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About this question

Topic
Integration, A-Level Further Mathematics (syllabus 9231). Structured question, 7 marks.
Source
A-Level Further Mathematics, Oct/Nov 2019 Paper 1 Variant 2, question 3.

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