| Exam Board | OCR |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2008 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Integration by Parts |
| Type | Integration of x^n·ln(x) |
| Difficulty | Standard +0.3 This is a straightforward application of integration by parts with the standard choice u = ln(x), dv = x^4 dx. The technique is routine for C4 level, requiring one application of integration by parts followed by simple polynomial integration. The definite integral evaluation at limits 1 and e is clean, making this slightly easier than average but still requiring careful execution. |
| Spec | 1.08i Integration by parts |
2 Find the exact value of $\int _ { 1 } ^ { \mathrm { e } } x ^ { 4 } \ln x \mathrm {~d} x$.
\hfill \mbox{\textit{OCR C4 2008 Q2 [5]}}