| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2012 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Integration by Parts |
| Type | Show that integral equals expression |
| Difficulty | Standard +0.3 This is a straightforward integration by parts question with a clean trigonometric integrand. While it requires careful execution of the technique twice and evaluation at the limits, it follows a standard pattern with no conceptual surprises. The 5 marks reflect routine algebraic manipulation rather than problem-solving insight, making it slightly easier than average. |
| Spec | 1.08i Integration by parts |
Show that $\int_0^{\frac{\pi}{2}} x \cos \frac{1}{2} x \, dx = \frac{\sqrt{2}}{2} \pi + 2\sqrt{2} - 4$. [5]
\hfill \mbox{\textit{OCR MEI C3 2012 Q3 [5]}}