OCR MEI C3 2008 June — Question 4 4 marks

Exam BoardOCR MEI
ModuleC3 (Core Mathematics 3)
Year2008
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicIntegration by Substitution
TypeShow definite integral equals specific value (algebraic/exponential substitution)
DifficultyModerate -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.
Spec1.08h Integration by substitution

4 Show that \(\int _ { 1 } ^ { 4 } \frac { x } { x ^ { 2 } + 2 } \mathrm {~d} x = \frac { 1 } { 2 } \ln 6\).

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]}}