| Exam Board | Edexcel |
|---|---|
| Module | C34 (Core Mathematics 3 & 4) |
| Year | 2018 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Integration by Parts |
| Type | Independent multi-part (different techniques) |
| Difficulty | Moderate -0.8 Both parts are routine textbook exercises: (i) requires algebraic simplification before integrating term-by-term, and (ii) is a standard one-step integration by parts with no complications. These are direct applications of techniques with no problem-solving or insight required, making them easier than average A-level questions. |
| Spec | 1.08b Integrate x^n: where n != -1 and sums1.08c Integrate e^(kx), 1/x, sin(kx), cos(kx)1.08i Integration by parts |
\begin{enumerate}
\item (i) Find
\end{enumerate}
$$\int \frac { 2 x ^ { 2 } + 5 x + 1 } { x ^ { 2 } } \mathrm {~d} x , \quad x > 0$$
(ii) Find
$$\int x \cos 2 x \mathrm {~d} x$$
\hfill \mbox{\textit{Edexcel C34 2018 Q1 [6]}}