| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2023 |
| Session | June |
| Paper | Download PDF ↗ |
| Topic | Areas by integration |
| Type | Simpson's rule estimation |
| Difficulty | Moderate -0.8 This is a straightforward application of Simpson's rule with clear instructions (4 intervals, function given). Part (a) requires only mechanical substitution into the Simpson's rule formula, and part (b) is a simple comparison. While it's Further Maths content, Simpson's rule is a standard numerical method requiring no problem-solving or insight—just careful arithmetic. |
| Spec | 1.09f Trapezium rule: numerical integration |
\begin{enumerate}
\item (a) Use Simpson's rule with 4 intervals to find an estimate for
\end{enumerate}
$$\int _ { 0 } ^ { 2 } \mathrm { e } ^ { \sin ^ { 2 } x } \mathrm {~d} x$$
Give your answer to 3 significant figures.
Given that $\int _ { 0 } ^ { 2 } \mathrm { e } ^ { \mathrm { sin } ^ { 2 } x } \mathrm {~d} x = 3.855$ to 4 significant figures,\\
(b) comment on the accuracy of your answer to part (a).
\begin{center}
\end{center}
\hfill \mbox{\textit{Edexcel FP1 2023 Q1}}