| Exam Board | OCR |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Integration by Substitution |
| Type | Show definite integral equals specific value (trigonometric substitution) |
| Difficulty | Standard +0.3 This is a standard C4 integration by substitution question with a given substitution and target answer. Students must apply the substitution correctly, simplify using trigonometric identities (1 + tan²u = sec²u), integrate a standard form, and adjust limits. While it requires careful algebraic manipulation across multiple steps, the substitution is provided and the techniques are routine for C4 level, making it slightly easier than average. |
| Spec | 1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.08h Integration by substitution |
Use the substitution $x = 2 \tan u$ to show that
$$\int_0^2 \frac{x^2}{x^2 + 4} \, dx = \frac{1}{2}(4 - \pi).$$ [8]
\hfill \mbox{\textit{OCR C4 Q6 [8]}}