| Exam Board | AQA |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2013 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Indefinite & Definite Integrals |
| Type | Numerical integration comparison |
| Difficulty | Moderate -0.3 This is a straightforward application of the mid-ordinate rule with clear instructions (5 strips, 3 sf). Part (a) requires systematic calculation but no conceptual difficulty. Part (b) tests understanding of whether the rule over/underestimates for a convex function, which is standard C3 content. Slightly easier than average due to the routine nature of numerical methods questions. |
| Spec | 1.09f Trapezium rule: numerical integration |
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}
\begin{enumerate}[label=(\alph*)]
\item 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.
\item 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)
\end{enumerate}
\hfill \mbox{\textit{AQA C3 2013 Q5 [6]}}