5 The diagram shows a sketch of the graph of \(y = \sqrt { 27 + x ^ { 3 } }\).
\includegraphics[max width=\textwidth, alt={}, center]{063bbfa5-df49-44a1-8143-5e076397f63f-04_762_988_365_534}
- The area of the shaded region, bounded by the curve, the \(x\)-axis and the lines \(x = 0\) and \(x = 4\), is given by \(\int _ { 0 } ^ { 4 } \sqrt { 27 + x ^ { 3 } } \mathrm {~d} x\).
Use the mid-ordinate rule with five strips to find an estimate for this area. Give your answer to three significant figures.
- With the aid of a diagram, explain whether the mid-ordinate rule applied in part (a) gives an estimate which is smaller than or greater than the area of the shaded region.
(2 marks)