| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2024 |
| Session | February |
| Marks | 7 |
| Topic | Integration with Partial Fractions |
| Type | Improper integrals with partial fractions (infinite limit) |
| Difficulty | Standard +0.3 This is a straightforward Further Maths improper integral question. Part (a) requires simple recall (infinite upper limit). Part (b) involves routine partial fractions, integration of 1/x terms, and evaluating a limit as the upper bound tends to infinity—all standard techniques with no novel insight required. The 7 total marks reflect mechanical steps rather than conceptual difficulty, making this easier than average. |
| Spec | 4.08c Improper integrals: infinite limits or discontinuous integrands |
\begin{enumerate}[label=(\alph*)]
\item Explain why $\int_1^\infty \frac{1}{x(2x + 5)} dx$ is an improper integral. [1]
\item Prove that
$$\int_1^\infty \frac{1}{x(2x + 5)} dx = a \ln b$$
where $a$ and $b$ are rational numbers to be determined. [6]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM Pure 2024 Q6 [7]}}