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Date November 2008 Marks available 5 Reference code 08N.1.hl.TZ0.5
Level HL only Paper 1 Time zone TZ0
Command term Calculate Question number 5 Adapted from N/A

Question

Calculate the exact value of e1x2lnxdx .

Markscheme

Recognition of integration by parts     M1

x2lnxdx=[x33lnx]x33×1xdx     A1A1

=[x33lnx]x23dx

=[x33lnxx39]     A1

e1x2lnxdx=(e33e39)(019)(=2e3+19)     A1

[5 marks]

Examiners report

Most candidates recognised that a method of integration by parts was appropriate for this question. However, although a good number of correct answers were seen, a number of candidates made algebraic errors in the process. A number of students were also unable to correctly substitute the limits.

Syllabus sections

Topic 6 - Core: Calculus » 6.7 » Integration by parts.

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