| Exam Board | OCR |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2010 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Integration by Substitution |
| Type | Definite integral with simple linear/polynomial substitution |
| Difficulty | Moderate -0.3 This is a straightforward substitution question where the substitution is given explicitly. Students need to find du/dt = 1/t, change limits (t=1 gives u=2, t=e gives u=3), and integrate 1/u² which is standard. The mechanics are routine for C4, though slightly easier than average since the substitution works cleanly without algebraic manipulation. |
| Spec | 1.08h Integration by substitution |
4 Use the substitution $u = 2 + \ln t$ to find the exact value of
$$\int _ { 1 } ^ { \mathrm { e } } \frac { 1 } { t ( 2 + \ln t ) ^ { 2 } } \mathrm {~d} t$$
\hfill \mbox{\textit{OCR C4 2010 Q4 [6]}}