- In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{7e38e2ed-ab5f-4906-940e-4b02c6992164-22_568_1192_376_440}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows the curve with equation
$$y = \ln \left( \tanh \frac { x } { 2 } \right) \quad 1 \leqslant x \leqslant 2$$
- Show that the length, \(s\), of the curve is given by
$$s = \int _ { 1 } ^ { 2 } \operatorname { coth } x \mathrm {~d} x$$
- Hence show that
$$s = \ln \left( \mathrm { e } + \frac { 1 } { \mathrm { e } } \right)$$