| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Session | Specimen |
| 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 trigonometric substitution that's given to the student. While it requires multiple steps (finding dx/dθ, changing limits, using trig identities like sec²θ = 1+tan²θ, and integrating cos²θ), these are all routine techniques for C4. The substitution is provided rather than requiring insight to choose it, and the working follows a predictable path. Slightly easier than average due to the scaffolding provided. |
| Spec | 1.08h Integration by substitution |
3. Use the substitution $x = \tan \theta$ to show that
$$\int _ { 0 } ^ { 1 } \frac { 1 } { \left( 1 + x ^ { 2 } \right) ^ { 2 } } \mathrm {~d} x = \frac { \pi } { 8 } + \frac { 1 } { 4 }$$
(8)\\
\hfill \mbox{\textit{Edexcel C4 Q3 [8]}}