| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2024 |
| Session | February |
| Marks | 6 |
| Topic | Integration using inverse trig and hyperbolic functions |
| Type | Partial fractions then inverse trig integration |
| Difficulty | Challenging +1.8 This question requires partial fraction decomposition of a quartic denominator (factoring 1-x⁴ as difference of squares), integration of resulting terms including arctangent, and careful algebraic manipulation to express the answer in the specified form. The multi-step nature, need for strategic factorization, and exact evaluation at non-trivial limits make this substantially harder than average, though the techniques are all standard Further Maths content. |
| Spec | 4.08f Integrate using partial fractions |
Show that $\int_0^{\frac{1}{\sqrt{3}}} \frac{4}{1-x^4} dx = \ln(a + \sqrt{b}) + \frac{\pi}{c}$ where $a$, $b$ and $c$ are integers to be determined. [6]
\hfill \mbox{\textit{SPS SPS FM Pure 2024 Q14 [6]}}