| Exam Board | CAIE |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2011 |
| Session | November |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Volumes 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\\
(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}}