7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{094b3c91-1460-44a2-b9d6-4de90d3adfa0-13_593_1292_118_328}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
The curves shown in Figure 1 have equations
$$y = 6 \cosh x \text { and } y = 9 - 2 \sinh x$$
- Using the definitions of \(\sinh x\) and \(\cosh x\) in terms of \(\mathrm { e } ^ { x }\), find exact values for the \(x\)-coordinates of the two points where the curves intersect.
The finite region between the two curves is shown shaded in Figure 1.
- Using calculus, find the area of the shaded region, giving your answer in the form \(a \ln b + c\), where \(a , b\) and \(c\) are integers.