OCR C4 — Question 3 8 marks

Exam BoardOCR
ModuleC4 (Core Mathematics 4)
Marks8
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicIntegration by Substitution
TypeShow definite integral equals specific value (algebraic/exponential substitution)
DifficultyStandard +0.3 This is a straightforward integration by substitution question where the substitution is given explicitly. Students must find du/dx, change limits, express the integrand in terms of u, and evaluate a standard power integral. While it requires careful algebraic manipulation and multiple steps, it follows a completely standard procedure with no conceptual surprises, making it slightly easier than average.
Spec1.08d Evaluate definite integrals: between limits1.08h Integration by substitution

3. Using the substitution \(u = \mathrm { e } ^ { x } - 1\), show that $$\int _ { \ln 2 } ^ { \ln 5 } \frac { \mathrm { e } ^ { 2 x } } { \sqrt { \mathrm { e } ^ { x } - 1 } } \mathrm {~d} x = \frac { 20 } { 3 }$$

3. Using the substitution $u = \mathrm { e } ^ { x } - 1$, show that

$$\int _ { \ln 2 } ^ { \ln 5 } \frac { \mathrm { e } ^ { 2 x } } { \sqrt { \mathrm { e } ^ { x } - 1 } } \mathrm {~d} x = \frac { 20 } { 3 }$$

\hfill \mbox{\textit{OCR C4  Q3 [8]}}