4 Fig. 4 shows the graph of \(y = \sqrt { 1 + x ^ { 3 } }\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{95eb3bcc-6d3c-4f7e-9b27-5e046ab57ec5-05_544_639_338_248}
\captionsetup{labelformat=empty}
\caption{Fig. 4}
\end{figure}
- Use the trapezium rule with \(h = 0.5\) to find an estimate of \(\int _ { - 1 } ^ { 0 } \sqrt { 1 + x ^ { 3 } } \mathrm {~d} x\), giving your answer correct to 6 decimal places.
- State whether your answer to part (a) is an under-estimate or an over-estimate, justifying your answer.