7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8d67f716-c8af-4460-8a6b-62073ba9b825-13_695_986_121_497}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Diagram not drawn to scale
Figure 1 shows a sketch of part of the curve with equation \(y = \frac { 1 } { \sqrt { 2 x + 5 } } , x > - 2.5\)
The finite region \(R\), shown shaded in Figure 1, is bounded by the curve, the \(x\)-axis and the lines with equations \(x = 2\) and \(x = 5\)
- Use the trapezium rule with three strips of equal width to find an estimate for the area of \(R\), giving your answer to 3 decimal places.
- Use calculus to find the exact area of \(R\).
- Hence calculate the magnitude of the error of the estimate found in part (a), giving your answer to one significant figure.