| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Areas by integration |
| Type | Simpson's rule estimation |
| Difficulty | Moderate -0.8 This is a straightforward C3 question testing two standard techniques: (i) integration by substitution or recognition of a standard form (reverse chain rule), and (ii) mechanical application of Simpson's rule. Both parts are routine procedures with no problem-solving required, making it easier than average, though not trivial since it requires careful execution of the Simpson's rule formula. |
| Spec | 1.08h Integration by substitution1.09f Trapezium rule: numerical integration |
The integral $I$ is defined by
$$I = \int_0^{13} (2x + 1)^{\frac{3}{2}} \, dx.$$
\begin{enumerate}[label=(\roman*)]
\item Use integration to find the exact value of $I$. [4]
\item Use Simpson's rule with two strips to find an approximate value for $I$. Give your answer correct to 3 significant figures. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR C3 Q4 [7]}}