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Date	May 2018	Marks available	3	Reference code	18M.2.SL.TZ2.S_3
Level	Standard Level	Paper	Paper 2	Time zone	Time zone 2
Command term	Find	Question number	S_3	Adapted from	N/A

Question

Let $f\left( x \right) = \,\,{\text{sin}}\,\left( {{e^x}} \right)$ for 0 ≤ $x$ ≤ 1.5. The following diagram shows the graph of $f$ .

Find the x-intercept of the graph of $f$ .

[2]

The region enclosed by the graph of $f$ , the y-axis and the x-axis is rotated 360° about the x-axis.

Find the volume of the solid formed.

[3]

Markscheme

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

valid approach (M1)
eg $f\left( x \right) = 0,\,\,\,\,{e^x} = 180$ or 0…

1.14472

$x = {\text{ln}}\,\pi$ (exact), 1.14 A1 N2

[2 marks]

attempt to substitute either their limits or the function into formula involving ${f^2}$ . (M1)

eg ${\int_0^{1.14} {{f^2},\,\,\pi \int {\left( {{\text{sin}}\,\left( {{e^x}} \right)} \right)} } ^2}dx,\,\,0.795135$

2.49799

volume = 2.50 A2 N3

[3 marks]

Examiners report

[N/A]

Syllabus sections

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

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Topic 5—Calculus » AHL 5.12—Areas under a curve onto x or y axis. Volumes of revolution about x and y

Topic 5—Calculus

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