A2 June 2019 Paper 1 Q6
6 In this question you must show detailed reasoning.
Find \(\displaystyle\int_2^{\infty} \frac{1}{4 + x^2}\,\mathrm{d}x\). [4]
| Scheme | Marks | AO |
|---|---|---|
| DR \(\displaystyle I = \int_2^{\infty} \frac{1}{4 + x^2}\,\mathrm{d}x = \left[\frac{1}{2}\arctan\frac{x}{2}\right]_2^{\infty}\) | B1 | 1.1b |
| as \(x \to \infty\), \(\arctan\frac{1}{2}x \to \frac{1}{2}\pi\) | B2 | 2.4, 2.2a |
| \(I = \dfrac{1}{8}\pi\) | B1 | 1.1b |
| [4] |
Notes
B1: \(\left[\frac{1}{2}\arctan\frac{x}{2}\right]\)
B2: if \(\frac{1}{2}\pi\) only B1 (soi)
B1: 0.393 or better; allow B1 if unsupported