17.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8053bd07-c2b2-4ada-ae0e-8ab6b8466c78-36_613_860_189_653}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
Figure 3 shows a sketch of the curve with equation \(y = 2 ^ { x ^ { 2 } } - x\).
The finite region \(R\), shown shaded in Figure 3, is bounded by the curve, the line with equation \(x = - 0.5\), the \(x\)-axis and the line with equation \(x = 1.5\).
- The trapezium rule with four strips is used to find an estimate for the area of \(R\).
Explain whether the estimate for R is an underestimate or overestimate to the true value for the area of \(R\).
The estimate for R is found to be 2.58 .
Using this value, and showing your working, - estimate the value of \(\int _ { - 0.5 } ^ { 1.5 } \left( 2 ^ { x ^ { 2 } + 1 } + 2 x \right) d x\).
[0pt]
[BLANK PAGE]
[0pt]
[BLANK PAGE]
[0pt]
[BLANK PAGE]