2. The curve \(C\) has equation
$$y = 8 - 2 ^ { x - 1 } , \quad 0 \leqslant x \leqslant 4$$
- Complete the table below with the value of \(y\) corresponding to \(x = 1\)
- Use the trapezium rule, with all the values of \(y\) in the completed table, to find an approximate value for \(\int _ { 0 } ^ { 4 } \left( 8 - 2 ^ { x - 1 } \right) \mathrm { d } x\)
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{582cda45-80fc-43a8-90e6-1cae08cb1534-03_650_606_1016_671}
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\caption{Figure 1}
\end{figure}
Figure 1 shows a sketch of the curve \(C\) with equation \(y = 8 - 2 ^ { x - 1 } , \quad 0 \leqslant x \leqslant 4\)
The curve \(C\) meets the \(x\)-axis at the point \(A\) and meets the \(y\)-axis at the point \(B\).
The region \(R\), shown shaded in Figure 1, is bounded by the curve \(C\) and the straight line through \(A\) and \(B\). - Use your answer to part (b) to find an approximate value for the area of \(R\).