CAIE FP1 2011 November — Question 9

Exam BoardCAIE
ModuleFP1 (Further Pure Mathematics 1)
Year2011
SessionNovember
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicVolumes of Revolution

9 The curve \(C\) has equation \(y = \frac { 1 } { 2 } \left( \mathrm { e } ^ { x } + \mathrm { e } ^ { - x } \right)\) for \(0 \leqslant x \leqslant \ln 5\). Find
  1. the mean value of \(y\) with respect to \(x\) over the interval \(0 \leqslant x \leqslant \ln 5\),
  2. the arc length of \(C\),
  3. the surface area generated when \(C\) is rotated through \(2 \pi\) radians about the \(x\)-axis.

9 The curve $C$ has equation $y = \frac { 1 } { 2 } \left( \mathrm { e } ^ { x } + \mathrm { e } ^ { - x } \right)$ for $0 \leqslant x \leqslant \ln 5$. Find\\
(i) the mean value of $y$ with respect to $x$ over the interval $0 \leqslant x \leqslant \ln 5$,\\
(ii) the arc length of $C$,\\
(iii) the surface area generated when $C$ is rotated through $2 \pi$ radians about the $x$-axis.

\hfill \mbox{\textit{CAIE FP1 2011 Q9}}