| Exam Board | AQA |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Year | 2013 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Integration with Partial Fractions |
| Type | Improper integrals with infinite upper limit (combined rational terms) |
| Difficulty | Challenging +1.2 This is a Further Maths FP3 question requiring improper integral evaluation with standard techniques (logarithmic integration and limits). While it involves multiple steps—recognizing standard integral forms, applying limits to infinity, and simplifying logarithms—each component is routine for FP3 students. The algebraic manipulation is straightforward once the antiderivative is found. Slightly above average difficulty due to the improper integral context and need for careful limit evaluation, but no novel insight required. |
| Spec | 1.06f Laws of logarithms: addition, subtraction, power rules4.08c Improper integrals: infinite limits or discontinuous integrands |
4 Evaluate the improper integral
$$\int _ { 0 } ^ { \infty } \left( \frac { 2 x } { x ^ { 2 } + 4 } - \frac { 4 } { 2 x + 3 } \right) \mathrm { d } x$$
showing the limiting process used and giving your answer in the form $\ln k$, where $k$ is a constant.
\hfill \mbox{\textit{AQA FP3 2013 Q4 [6]}}