| Exam Board | OCR |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | 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 a standard x^n·ln(x) form. The technique is routine for C4 students: let u=ln(x), dv=x²dx, then integrate and evaluate at limits. It requires one integration by parts followed by basic polynomial integration and substitution of limits—slightly above average due to the logarithm and definite integral evaluation, but still a textbook exercise. |
| Spec | 1.08i Integration by parts |
3. Find the exact value of
$$\int _ { 1 } ^ { 3 } x ^ { 2 } \ln x d x$$
\hfill \mbox{\textit{OCR C4 Q3 [5]}}