| Exam Board | OCR |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Integration by Substitution |
| Type | Definite integral with simple linear/polynomial substitution |
| Difficulty | Standard +0.3 Part (i) requires knowing the identity tan²θ = sec²θ - 1 and integrating with a linear substitution (routine but not trivial). Part (ii) is a standard substitution exercise with clear guidance on the substitution to use. Both parts are straightforward applications of techniques with no novel problem-solving required, making this slightly easier than average. |
| Spec | 1.08c Integrate e^(kx), 1/x, sin(kx), cos(kx)1.08h Integration by substitution |
6. (i) Find $\int \tan ^ { 2 } 3 x \mathrm {~d} x$.\\
(ii) Using the substitution $u = x ^ { 2 } + 4$, evaluate
$$\int _ { 0 } ^ { 2 } \frac { 5 x } { \left( x ^ { 2 } + 4 \right) ^ { 2 } } d x$$
\hfill \mbox{\textit{OCR C4 Q6 [9]}}