A2 June 2025 Paper 1 Q6
6 Use Simpson’s rule with 5 ordinates to find an approximation to
\[\int_0^2 \frac{1}{\sqrt{1 + x^4}}\,\mathrm{d}x\]Give your answer to three decimal places. [3 marks]
| Scheme | Marks | AO |
|---|---|---|
| Obtains exactly five values of \(y\) | M1 | 1.1a |
| Uses the Simpson’s rule formula correctly for their five \(y\) values and their \(h\) | M1 | 1.1a |
| Obtains 1.360 Condone 1.36 Condone AWRT 1.360 | A1 | 1.1b |
| (3 marks) |
Typical solution
| \(x\) | 0 | 0.5 | 1 | 1.5 | 2 |
| \(y\) | 1 | 0.9701 | 0.7071 | 0.4061 | 0.2425 |
| \(y\) | 1 | \(\dfrac{4\sqrt{17}}{17}\) | \(\dfrac{\sqrt{2}}{2}\) | \(\dfrac{4\sqrt{97}}{97}\) | \(\dfrac{\sqrt{17}}{17}\) |