| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Numerical integration |
| Type | Complete table then apply trapezium rule |
| Difficulty | Standard +0.3 This is a straightforward multi-part question requiring integration by parts (standard technique for xe^(2x)), substituting values into a function, and applying the trapezium rule formula. All components are routine C4 procedures with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.08i Integration by parts1.09f Trapezium rule: numerical integration |
| \(x\) | 0 | 0.2 | 0.4 | 0.6 | 0.8 | 1 |
| \(y = x \mathrm { e } ^ { 2 x }\) | 0 | 0.29836 | 1.99207 | 7.38906 |
5.
\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\includegraphics[alt={},max width=\textwidth]{a0bd937d-b92e-41d0-abfa-ec83ccda058a-007_586_1079_260_427}
\end{center}
\end{figure}
Figure 1 shows the graph of the curve with equation
$$y = x \mathrm { e } ^ { 2 x } , \quad x \geqslant 0$$
The finite region $R$ bounded by the lines $x = 1$, the $x$-axis and the curve is shown shaded in Figure 1.
\begin{enumerate}[label=(\alph*)]
\item Use integration to find the exact value for the area of $R$.
\item Complete the table with the values of $y$ corresponding to $x = 0.4$ and 0.8 .
\begin{center}
\begin{tabular}{ | l | l | l | l | l | l | l | }
\hline
$x$ & 0 & 0.2 & 0.4 & 0.6 & 0.8 & 1 \\
\hline
$y = x \mathrm { e } ^ { 2 x }$ & 0 & 0.29836 & & 1.99207 & & 7.38906 \\
\hline
\end{tabular}
\end{center}
\item Use the trapezium rule with all the values in the table to find an approximate value for this area, giving your answer to 4 significant figures.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C4 Q5}}