| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2008 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Integration by Substitution |
| Type | Show definite integral equals specific value (algebraic/exponential substitution) |
| Difficulty | Moderate -0.3 This is a straightforward integration by substitution question where the substitution u = x² + 2 is strongly suggested by the integrand structure (numerator is derivative of denominator's inner function). It requires recognizing the pattern, executing a standard substitution, and evaluating definite integral limits—all routine C3 techniques with no problem-solving insight needed. Slightly easier than average due to the clear structure and 'show that' format providing the target answer. |
| Spec | 1.08h Integration by substitution |
4 Show that $\int _ { 1 } ^ { 4 } \frac { x } { x ^ { 2 } + 2 } \mathrm {~d} x = \frac { 1 } { 2 } \ln 6$.
\hfill \mbox{\textit{OCR MEI C3 2008 Q4 [4]}}