2.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{bb604886-6671-441a-b03d-427b5176df6e-03_606_1271_212_335}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
The curve \(C\), shown in Figure 1, has equation
$$y = \frac { 1 } { 3 } \cosh 3 x , \quad 0 \leqslant x \leqslant \ln a$$
where \(a\) is a constant and \(a > 1\)
Using calculus, show that the length of curve \(C\) is
$$k \left( a ^ { 3 } - \frac { 1 } { a ^ { 3 } } \right)$$
and state the value of the constant \(k\).