C4 January 2011 Q1
1. Use integration to find the exact value of \[\int_0^{\frac{\pi}{2}} x\sin 2x\,\mathrm{d}x\] (6)
| Scheme | Marks |
|---|---|
| \(\displaystyle\int x\sin 2x\,\mathrm{d}x = -\frac{x\cos 2x}{2} + \int \frac{\cos 2x}{2}\,\mathrm{d}x\) | M1 A1 A1 |
| \(= \quad \ldots \quad + \dfrac{\sin 2x}{4}\) | M1 |
| \(\Big[\ \ldots\ \Big]_0^{\frac{\pi}{2}} = \dfrac{\pi}{4}\) | M1 A1 |
| (6 marks) |