OCR MEI C3 2012 January — Question 3 5 marks

Exam BoardOCR MEI
ModuleC3 (Core Mathematics 3)
Year2012
SessionJanuary
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicIntegration by Parts
TypeShow that integral equals expression
DifficultyStandard +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.
Spec1.08i 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]

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]}}