| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2023 |
| Session | February |
| Marks | 4 |
| Topic | Integration using inverse trig and hyperbolic functions |
| Type | Improper integral to infinity with inverse trig |
| Difficulty | Standard +0.8 This is an improper integral requiring recognition of the arctan derivative form, evaluation of limits at infinity, and proper handling of the improper integral notation. While the integrand is a standard form, the infinite limit and need for rigorous limit notation elevates this above routine integration questions, though it remains a fairly standard Further Maths topic. |
| Spec | 4.08c Improper integrals: infinite limits or discontinuous integrands |
In this question you must show detailed reasoning.
Find $\int_{2}^{\infty} \frac{1}{4+x^2} \, dx$.
[4]
\hfill \mbox{\textit{SPS SPS FM Pure 2023 Q6 [4]}}