| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Numerical integration |
| Type | Complete table then apply trapezium rule |
| Difficulty | Moderate -0.3 This is a straightforward numerical methods question requiring routine application of the trapezium rule with given x-values. Part (a) involves simple calculator work evaluating e^x cos x at specific points, part (b) is standard trapezium rule application, and part (c) tests basic understanding of concavity. While it requires multiple steps and understanding of when trapezium rule over/underestimates, it involves no problem-solving or novel insight—just methodical execution of a standard technique, making it slightly easier than average. |
| Spec | 1.09f Trapezium rule: numerical integration |
\includegraphics{figure_2}
Figure 2 shows part of the curve with equation
$$y = e^x \cos x, \quad 0 \leq x \leq \frac{\pi}{2}.$$
The finite region $R$ is bounded by the curve and the coordinate axes.
\begin{enumerate}[label=(\alph*)]
\item Calculate, to 2 decimal places, the $y$-coordinates of the points on the curve where $x = 0$, $\frac{\pi}{6}$, $\frac{\pi}{3}$ and $\frac{\pi}{2}$. [3]
\item Using the trapezium rule and all the values calculated in part (a), find an approximation for the area of $R$. [4]
\item State, with a reason, whether your approximation underestimates or overestimates the area of $R$. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C4 Q3 [9]}}