| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2026 |
| Session | November |
| Marks | 4 |
| Topic | Integration by Substitution |
| Type | Algebraic manipulation before substitution |
| Difficulty | Standard +0.8 This requires completing the square to get the denominator into a form suitable for arctan integration, then applying limits carefully. It's a standard Further Maths technique but requires multiple steps (completing the square, recognizing the arctan form, substitution, and evaluating exact values) making it moderately harder than average A-level questions. |
| Spec | 4.08h Integration: inverse trig/hyperbolic substitutions |
In this question you must show detailed reasoning.
Evaluate $\int_0^{\frac{1}{2}} \frac{2}{x^2 - x + 1} dx$. Give your answer in exact form. [4]
\hfill \mbox{\textit{SPS SPS FM Pure 2026 Q7 [4]}}