| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Numerical integration |
| Type | Complete table then apply trapezium rule |
| Difficulty | Moderate -0.3 This is a straightforward application of the trapezium rule with minimal complexity. Part (a) requires simple calculator substitution into a given function, and part (b) is a direct application of the trapezium rule formula with equally-spaced ordinates. The question involves no problem-solving, conceptual challenges, or novel insights—just routine execution of a standard numerical method. It's slightly easier than average due to its mechanical nature and clear structure. |
| Spec | 1.09f Trapezium rule: numerical integration |
| \(x\) | 0 | 0.5 | 1 | 1.5 | 2 |
| \(y\) | 1 | 1.216 | \(p\) | 1.413 | \(q\) |
The following is a table of values for $y = \sqrt{1 + \sin x}$, where $x$ is in radians.
\begin{tabular}{|c|c|c|c|c|c|}
\hline
$x$ & 0 & 0.5 & 1 & 1.5 & 2 \\
\hline
$y$ & 1 & 1.216 & $p$ & 1.413 & $q$ \\
\hline
\end{tabular}
\begin{enumerate}[label=(\alph*)]
\item Find the value of $p$ and the value of $q$. [2]
\item Use the trapezium rule and all the values of $y$ in the completed table to obtain an estimate of $I$, where
$$I = \int_0^2 \sqrt{1 + \sin x} \, dx.$$ [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C4 Q9 [6]}}