| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Numerical integration |
| Type | Apply trapezium rule to given table |
| Difficulty | Moderate -0.8 This is a straightforward application of the trapezium rule with clearly specified values. Students must square the given voltages, apply the standard trapezium rule formula with h=0.25, then take a square root. It requires only routine procedural steps with no problem-solving or conceptual challenges beyond basic formula application. |
| Spec | 1.09f Trapezium rule: numerical integration |
| \(t\) | 0 | 0.25 | 0.5 | 0.75 | 1 |
| \(V\) | -48 | 207 | 37 | -161 | -29 |
| \(V^2\) |
A measure of the effective voltage, $M$ volts, in an electrical circuit is given by
$$M^2 = \int_0^1 V^2 \, dt$$
where $V$ volts is the voltage at time $t$ seconds. Pairs of values of $V$ and $t$ are given in the following table.
\begin{tabular}{|c|c|c|c|c|c|}
\hline
$t$ & 0 & 0.25 & 0.5 & 0.75 & 1 \\
\hline
$V$ & -48 & 207 & 37 & -161 & -29 \\
\hline
$V^2$ & & & & & \\
\hline
\end{tabular}
Use the trapezium rule with five values of $V^2$ to estimate the value of $M$.
[6]
\hfill \mbox{\textit{Edexcel C4 Q1 [6]}}