7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ae871952-f525-44e6-8bac-09308aa1964f-26_615_867_292_534}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows a sketch of part of the curve with equation
$$y = \frac { x + 7 } { \sqrt { 2 x - 3 } } \quad x > \frac { 3 } { 2 }$$
The region \(R\), shown shaded in Figure 1, is bounded by the curve, the line with equation \(x = 4\), the \(x\)-axis and the line with equation \(x = 6\)
- Use the trapezium rule with 4 strips of equal width to find an estimate for the area of \(R\), giving your answer to 2 decimal places.
- Using the substitution \(u = 2 x - 3\), or otherwise, use calculus to find the exact area of \(R\), giving your answer in the form \(a + b \sqrt { 5 }\), where \(a\) and \(b\) are constants to be found.