| Date | May 2018 | Marks available | 3 | Reference code | 18M.2.sl.TZ2.3 |
| Level | SL only | Paper | 2 | Time zone | TZ2 |
| Command term | Find | Question number | 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]
a.
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]
b.
Markscheme
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]
a.
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]
b.
Examiners report
[N/A]
a.
[N/A]
b.
Syllabus sections
Topic 2 - Functions and equations » 2.2 » Investigation of key features of graphs, such as maximum and minimum values, intercepts, horizontal and vertical asymptotes, symmetry, and consideration of domain and range.
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