| Exam Board | AQA |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Year | 2010 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Integration with Partial Fractions |
| Type | Improper integrals with infinite upper limit (exponential/IBP) |
| Difficulty | Standard +0.3 This is a straightforward Further Maths improper integral question requiring standard integration by parts followed by routine limit evaluation. Part (a) tests definition recall, part (b) is a textbook integration by parts example, and part (c) applies a standard limiting process. While it's Further Maths content, the techniques are mechanical with no novel insight required, making it slightly easier than average overall. |
| Spec | 1.08i Integration by parts4.08c Improper integrals: infinite limits or discontinuous integrands |
3
\begin{enumerate}[label=(\alph*)]
\item Explain why $\int _ { 1 } ^ { \infty } 4 x \mathrm { e } ^ { - 4 x } \mathrm {~d} x$ is an improper integral.
\item Find $\quad \int 4 x \mathrm { e } ^ { - 4 x } \mathrm {~d} x$.
\item Hence evaluate $\int _ { 1 } ^ { \infty } 4 x \mathrm { e } ^ { - 4 x } \mathrm {~d} x$, showing the limiting process used.
\end{enumerate}
\hfill \mbox{\textit{AQA FP3 2010 Q3 [7]}}