| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2021 |
| Session | November |
| Marks | 4 |
| Topic | Integration using inverse trig and hyperbolic functions |
| Type | Trigonometric substitution to simplify integral |
| Difficulty | Standard +0.8 This is a standard Further Maths integration technique requiring the substitution x = 4sin(θ), followed by using a trigonometric identity to simplify (16-x²)^(3/2) = 64cos³(θ), then integrating sec²(θ). While mechanical, it requires careful handling of limits and multiple steps, placing it moderately above average difficulty but still within the standard FM integration repertoire. |
| Spec | 4.08h Integration: inverse trig/hyperbolic substitutions |
Use a trigonometrical substitution to show that
$$\int_0^2 \frac{1}{(16 - x^2)^{\frac{3}{2}}} dx = \frac{1}{16\sqrt{3}}$$
[4 marks]
\hfill \mbox{\textit{SPS SPS FM 2021 Q5 [4]}}