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Date November 2017 Marks available 2 Reference code 17N.2.SL.TZ0.S_5
Level Standard Level Paper Paper 2 Time zone Time zone 0
Command term Find Question number S_5 Adapted from N/A

Question

Let f ( x ) = 6 ln ( x 2 + 2 ) , for x R . The graph of f passes through the point ( p ,   4 ) , where p > 0 .

Find the value of p .

[2]
a.

The following diagram shows part of the graph of f .

N17/5/MATME/SP2/ENG/TZ0/05.b

The region enclosed by the graph of f , the x -axis and the lines x = p and x = p is rotated 360° about the x -axis. Find the volume of the solid formed.

[3]
b.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

valid approach     (M1)

eg f ( p ) = 4 , intersection with y = 4 ,   ± 2.32

2.32143

p = e 2 2 (exact), 2.32     A1     N2

[2 marks]

a.

attempt to substitute either their limits or the function into volume formula (must involve f 2 , accept reversed limits and absence of π and/or d x , but do not accept any other errors)     (M1)

eg 2.32 2.32 f 2 ,   π ( 6 ln ( x 2 + 2 ) ) 2 d x ,  105.675

331.989

volume = 332     A2     N3

[3 marks]

b.

Examiners report

[N/A]
a.
[N/A]
b.

Syllabus sections

Topic 5—Calculus » SL 5.5—Integration introduction, areas between curve and x axis
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