11 The region \(R\) enclosed by the lines \(x = 1 , x = 6 , y = 0\) and the curve
$$y = \ln ( 8 - x )$$
is shown shaded in Figure 3 below.
\begin{figure}[h]
\captionsetup{labelformat=empty}
\caption{Figure 3}
\includegraphics[alt={},max width=\textwidth]{08e1f291-7052-40a5-b7b2-13fd1d0137c2-17_419_869_598_587}
\end{figure}
All distances are measured in centimetres.
11
- Use a single trapezium to find an approximate value of the area of the shaded region, giving your answer in \(\mathrm { cm } ^ { 2 }\) to two decimal places.
[0pt]
[2 marks]
\section*{Question 11 continues on the next page}
11 - Shape \(B\) is made from four copies of region \(R\) as shown in Figure 4 below.
\begin{figure}[h]
\captionsetup{labelformat=empty}
\caption{Figure 4}
\includegraphics[alt={},max width=\textwidth]{08e1f291-7052-40a5-b7b2-13fd1d0137c2-18_707_711_438_667}
\end{figure}
Shape \(B\) is cut from metal of thickness 2 mm
The metal has a density of \(10.5 \mathrm {~g} / \mathrm { cm } ^ { 3 }\)
Use the trapezium rule with six ordinates to calculate an approximate value of the mass of Shape B.
Give your answer to the nearest gram.
11 - Without further calculation, give one reason why the mass found in part (b) may be:
11 - an underestimate.
11
- (ii) an overestimate.