| Exam Board | OCR |
|---|---|
| Module | H240/02 (Pure Mathematics and Statistics) |
| Year | 2018 |
| Session | December |
| Marks | 7 |
| Topic | Integration using inverse trig and hyperbolic functions |
| Type | Trigonometric substitution to simplify integral |
| Difficulty | Challenging +1.8 This is a non-standard integration question requiring trigonometric substitution (x = sin θ), followed by using double angle formulas and integrating trigonometric functions. While the technique is taught in S1/C4, it requires multiple steps, careful algebraic manipulation, and is significantly harder than routine integration questions. The 7-mark allocation confirms this is a substantial problem requiring extended working. |
| Spec | 1.05i Inverse trig functions: arcsin, arccos, arctan domains and graphs1.08h Integration by substitution |
Use a suitable trigonometric substitution to find $\int \frac{x^2}{\sqrt{1-x^2}} \text{d}x$. [7]
\hfill \mbox{\textit{OCR H240/02 2018 Q8 [7]}}