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O-LevelAdditional MathematicsDifferentiation and integration4037/21 · May/June 2012 · Q45 Marks

Find d/dx (x² lnx).

  1. (i)Find d/dx (x² lnx).[2]
  2. (ii)Hence, or otherwise, find ∫xlnx dx.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2012). The mark or mark type is shown in brackets.

  1. [2] (i) 2xlnx + x² x (1/x) B1 + B1
  2. [1] (ii) ∫(2x ln x + x)dx = x² ln x(+ c) M1
  3. [1] ∫xlnxdx = (1/2)(x² lnx(+c) - ∫xdx) M1
  4. [1] (1/2)x² lnx - (1/4)x²(+c) A1

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About this question

Topic
Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 5 marks.
Source
O-Level Additional Mathematics, May/June 2012 Paper 2 Variant 1, question 4.

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