SPS SPS FM Pure 2021 June — Question 5 5 marks

Exam BoardSPS
ModuleSPS FM Pure (SPS FM Pure)
Year2021
SessionJune
Marks5
TopicIntegration by Parts
TypeIntegration of x^n·ln(x)
DifficultyStandard +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.
Spec1.08i 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]

$\int_1^2 x^3 \ln(2x) dx$ 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]}}