| Exam Board | OCR |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Integration by Parts |
| Type | Independent multi-part (different techniques) |
| Difficulty | Standard +0.3 Part (i) is a standard substitution (u = 2 - x²) requiring recognition of the derivative in the numerator. Part (ii) requires integration by parts applied twice, which is a routine C4 technique. Both are textbook exercises with no novel insight required, making this slightly easier than average. |
| Spec | 1.08h Integration by substitution1.08i Integration by parts |
3. Find\\
(i) $\int \frac { x } { 2 - x ^ { 2 } } \mathrm {~d} x$,\\
(ii) $\int x ^ { 2 } \mathrm { e } ^ { - x } \mathrm {~d} x$.\\
\hfill \mbox{\textit{OCR C4 Q3 [8]}}