| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Indefinite & Definite Integrals |
| Type | Trapezium rule estimation |
| Difficulty | Standard +0.3 This is a straightforward C4 question combining integration by parts (a standard technique for xe^x) with trapezium rule application. Part (a) requires one integration by parts—a routine procedure at this level. Parts (b) and (c) involve calculator work and applying the trapezium rule formula with given values. The question is slightly easier than average because it's methodical with no conceptual surprises, though integration by parts elevates it slightly above pure recall. |
| Spec | 1.08i Integration by parts1.09f Trapezium rule: numerical integration |
| \(x\) | 0 | 0.2 | 0.4 | 0.6 | 0.8 |
| \(y = xe^x\) | 0 | 0.29836 | 1.99207 |
\includegraphics{figure_1}
Figure 1 shows the graph of the curve with equation
$$y = xe^x, \quad x \geq 0.$$
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 of the area for $R$. [5]
\item Complete the table with the values of $y$ corresponding to $x = 0.4$ and $0.8$.
\begin{tabular}{|c|c|c|c|c|c|}
\hline
$x$ & 0 & 0.2 & 0.4 & 0.6 & 0.8 \\
\hline
$y = xe^x$ & 0 & 0.29836 & & 1.99207 & \\
\hline
\end{tabular}
[1]
\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. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C4 Q5 [10]}}