| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2021 |
| Session | June |
| Marks | 5 |
| Topic | Integration by Parts |
| Type | Integration of x^n·ln(x) |
| Difficulty | Standard +0.3 This is a straightforward integration by parts question with a standard integrand (polynomial times logarithm). While it requires careful algebraic manipulation and evaluation at limits, it follows a well-practiced technique with no conceptual surprises, making it slightly easier than average for Further Maths students. |
| Spec | 1.08i Integration by parts |
$\int_1^2 x^3 \ln(2x) dx$ can be written in the form $p \ln 2 + q$, where $p$ and $q$ are rational numbers.
Find $p$ and $q$.
[5 marks]
\hfill \mbox{\textit{SPS SPS FM Pure 2021 Q5 [5]}}