| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indefinite & Definite Integrals |
| Type | Pure definite integration |
| Difficulty | Moderate -0.8 This is a straightforward C2 definite integration question requiring only basic polynomial integration and substitution of limits. It involves routine application of the power rule with no problem-solving or conceptual challenges, making it easier than average. |
| Spec | 1.08d Evaluate definite integrals: between limits |
| Answer | Marks | Guidance |
|---|---|---|
| \(= \left[\frac{1}{4}x^4 - \frac{2}{3}x^3 + 4x\right]_1^4\) | M1 A1 | |
| \(= \left(\frac{64}{3} - 40 + 16\right) - \left(\frac{1}{4} - \frac{2}{3} + 4\right) = -\frac{9}{2}\) | M1 A1 | (4) |
$= \left[\frac{1}{4}x^4 - \frac{2}{3}x^3 + 4x\right]_1^4$ | M1 A1 |
$= \left(\frac{64}{3} - 40 + 16\right) - \left(\frac{1}{4} - \frac{2}{3} + 4\right) = -\frac{9}{2}$ | M1 A1 | **(4)**\begin{enumerate}
\item Evaluate
\end{enumerate}
$$\int _ { 1 } ^ { 4 } \left( x ^ { 2 } - 5 x + 4 \right) d x .$$
\hfill \mbox{\textit{Edexcel C2 Q1 [4]}}