| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Integration by Parts |
| Type | Independent multi-part (different techniques) |
| Difficulty | Standard +0.3 This is a standard C4 partial fractions question followed by routine integration. Part (a) requires algebraic manipulation to find constants (standard technique), and part (b) involves integrating logarithmic terms after partial fractions decomposition. While it requires multiple steps and careful algebra, both techniques are core syllabus material with no novel insight needed, making it slightly easier than average. |
| Spec | 1.02y Partial fractions: decompose rational functions1.08j Integration using partial fractions |
\includegraphics{figure_1}
Figure 1 shows part of the curve with equation $y = f(x)$, where
$$f(x) = \frac{x^2 + 1}{(1 + x)(3 - x)}, \quad 0 \leq x < 3.$$
\begin{enumerate}[label=(\alph*)]
\item Given that $f(x) = A + \frac{B}{1 + x} + \frac{C}{3 - x}$, find the values of the constants $A$, $B$ and $C$. [4]
\end{enumerate}
The finite region $R$, shown in Fig. 1, is bounded by the curve with equation $y = f(x)$, the $x$-axis, the $y$-axis and the line $x = 2$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the area of $R$, giving your answer in the form $p + q \ln r$, where $p$, $q$ and $r$ are rational constants to be found. [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C4 Q20 [9]}}