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
=[x33lnx−x39] A1
⇒∫e1x2lnxdx=(e33−e39)−(0−19)(=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.