| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Integration by Parts |
| Type | Basic integration by parts |
| Difficulty | Moderate -0.3 Part (a) is a standard integration by parts exercise with a straightforward choice of u and dv, requiring only routine application of the formula. Part (b) adds a mild algebraic verification step using double-angle identities, but this is still within typical C4 expectations. The question is slightly easier than average due to its predictable structure and limited conceptual demand. |
| Spec | 1.05l Double angle formulae: and compound angle formulae1.08i Integration by parts |
\begin{enumerate}[label=(\alph*)]
\item Use integration by parts to find
$$\int x \cos 2x \, dx.$$ [4]
\item Prove that the answer to part $(a)$ may be expressed as
$$\frac{1}{2} \sin x (2x \cos x - \sin x) + C,$$
where $C$ is an arbitrary constant. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C4 Q18 [7]}}