| Exam Board | OCR |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 5 |
| 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 with a clear substitution (u = x² - 4). The working involves standard techniques: substituting, changing limits, integrating u^(1/2) to get (2/3)u^(3/2), and evaluating. While it requires competent execution of the substitution method, it's a textbook example with no conceptual challenges or novel insights required, making it slightly easier than average. |
| Spec | 1.08h Integration by substitution |
\begin{enumerate}
\item Show that
\end{enumerate}
$$\int _ { 2 } ^ { 4 } x \left( x ^ { 2 } - 4 \right) ^ { \frac { 1 } { 2 } } \mathrm {~d} x = 8 \sqrt { 3 }$$
\hfill \mbox{\textit{OCR C4 Q1 [5]}}