OCR H240/02 — Question 4 7 marks

Exam BoardOCR
ModuleH240/02 (Pure Mathematics and Statistics)
Marks7
PaperDownload PDF ↗
TopicPartial Fractions
TypePartial fractions with linear factors – decompose and integrate (definite)
DifficultyModerate -0.8 This is a straightforward partial fractions question with simple linear factors and a routine integration application. Part (a) requires standard algebraic manipulation to find constants A and B, while part (b) involves integrating to get logarithms and evaluating at given limits. This is a textbook exercise testing basic technique with no problem-solving insight required, making it easier than average.
Spec1.02y Partial fractions: decompose rational functions1.08j Integration using partial fractions

4
  1. Express \(\frac { 1 } { ( x - 1 ) ( x + 2 ) }\) in partial fractions
    [0pt] [2]
  2. In this question you must show detailed reasoning. Hence find \(\int _ { 2 } ^ { 3 } \frac { 1 } { ( x - 1 ) ( x + 2 ) } \mathrm { d } x\).
    Give your answer in its simplest form.

4
\begin{enumerate}[label=(\alph*)]
\item Express $\frac { 1 } { ( x - 1 ) ( x + 2 ) }$ in partial fractions\\[0pt]
[2]
\item In this question you must show detailed reasoning.

Hence find $\int _ { 2 } ^ { 3 } \frac { 1 } { ( x - 1 ) ( x + 2 ) } \mathrm { d } x$.\\
Give your answer in its simplest form.
\end{enumerate}

\hfill \mbox{\textit{OCR H240/02  Q4 [7]}}