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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=lnydu=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.

Syllabus sections

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