The curve $C$ has equation $y = \frac { 1 } { 2 } \left( \mathrm { e } ^ { x } + \mathrm { e } ^ { - x } \right)$ for $0 \leqslant x \leqslant 4$.\\
(i) The region $R$ is bounded by $C$, the $x$-axis, the $y$-axis and the line $x = 4$. Find, in terms of e, the coordinates of the centroid of the region $R$.\\

(ii) Show that $\frac { \mathrm { d } s } { \mathrm {~d} x } = \frac { 1 } { 2 } \left( \mathrm { e } ^ { x } + \mathrm { e } ^ { - x } \right)$, where $s$ denotes the arc length of $C$, and find the surface area generated when $C$ is rotated through $2 \pi$ radians about the $x$-axis.\\

\hfill \mbox{\textit{CAIE FP1 2017 Q12 EITHER}}