Date | May 2008 | Marks available | 6 | Reference code | 08M.2.hl.TZ1.9 |
Level | HL only | Paper | 2 | Time zone | TZ1 |
Command term | Find | Question number | 9 | Adapted from | N/A |
Question
By using an appropriate substitution find
∫tan(lny)ydy, y>0 .
Markscheme
Let u=lny⇒du=1ydy A1(A1)
∫tan(lny)ydy=∫tanudu A1
=∫sinucosudu=−ln|cosu|+c A1
EITHER
∫tan(lny)ydy=−ln|cos(lny)|+c A1A1
OR
∫tan(lny)ydy=ln|sec(lny)|+c A1A1
[6 marks]
Examiners report
Many candidates obtained the first three marks, but then attempted various methods unsuccessfully. Quite a few candidates attempted integration by parts rather than substitution. The candidates who successfully integrated the expression often failed to put the absolute value sign in the final answer.