| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Integration by Parts |
| Type | Basic integration by parts |
| Difficulty | Moderate -0.3 Part (a) is a standard textbook application of integration by parts with straightforward choices (u=x, dv=cos 2x dx). Part (b) requires algebraic manipulation using double-angle formulas to verify equivalence, adding modest complexity. Overall slightly easier than average due to the routine nature of the technique and clear structure. |
| Spec | 1.05l Double angle formulae: and compound angle formulae1.08i Integration by parts |
I notice you've provided "Question 2: 2" but there doesn't appear to be any actual mark scheme content to clean up.
Could you please provide the full extracted mark scheme content that needs to be cleaned? Please include the complete marking points, annotations (M1, A1, B1, etc.), and any guidance notes.2. (a) Use integration by parts to find
$$\int x \cos 2 x d x$$
(b) Prove that the answer to part (a) may be expressed as
$$\frac { 1 } { 2 } \sin x ( 2 x \cos x - \sin x ) + C ,$$
where $C$ is an arbitrary constant.\\
\hfill \mbox{\textit{Edexcel C4 Q2 [7]}}