| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Integration by Substitution |
| Type | Trigonometric substitution: direct evaluation |
| Difficulty | Challenging +1.2 This is a standard integration by substitution question with a given substitution. While it requires careful handling of the derivative dx = cos θ dθ, the algebraic simplification (1-sin²θ = cos²θ) is straightforward, and changing limits is routine. The 7 marks reflect multiple steps rather than conceptual difficulty. It's moderately above average because students must execute the full substitution process correctly and recognize the trigonometric simplification, but it follows a well-practiced template. |
| Spec | 1.08h Integration by substitution |
Use the substitution $x = \sin \theta$ to find the exact value of
$$\int_0^1 \frac{1}{(1-x^2)^{3/2}} dx.$$
[7]
\hfill \mbox{\textit{Edexcel C4 Q4 [7]}}