| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2011 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Integration by Parts |
| Type | Derivative then integrate by parts |
| Difficulty | Moderate -0.3 Part (i) is a straightforward quotient rule application with ln x, a standard C3 technique. Part (ii) is a routine integration by parts question with a clear hint in the structure. Both parts are textbook exercises requiring standard methods without problem-solving insight, making this slightly easier than average but not trivial due to the algebraic manipulation required. |
| Spec | 1.07q Product and quotient rules: differentiation1.08i Integration by parts |
\begin{enumerate}[label=(\roman*)]
\item Differentiate $\frac{\ln x}{x^2}$, simplifying your answer. [4]
\item Using integration by parts, show that $\int \frac{\ln x}{x^2} \, dx = -\frac{1}{x}(1 + \ln x) + c$. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C3 2011 Q3 [8]}}