| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2020 |
| Session | September |
| Marks | 4 |
| Topic | Standard Integrals and Reverse Chain Rule |
| Type | Polynomial division before integration |
| Difficulty | Moderate -0.3 This is a straightforward algebraic integration requiring polynomial division to split the integrand into 4 + (-3)/(x+3), then integrating to get 4x - 3ln|x+3|. Evaluating between limits involves basic logarithm laws. It's slightly easier than average as it's a standard technique with clear steps, though the algebraic manipulation and exact answer requirement prevent it from being trivial. |
| Spec | 1.02k Simplify rational expressions: factorising, cancelling, algebraic division1.08b Integrate x^n: where n != -1 and sums |
Using algebraic integration and making your method clear, find the exact value of
$$\int_1^5 \frac{4x + 9}{x + 3} \, dx = a + \ln b$$
where $a$ and $b$ are constants to be found
[4]
\hfill \mbox{\textit{SPS SPS FM 2020 Q3 [4]}}