| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 5 |
| 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 expansion of a quadratic bracket, term-by-term integration using basic power rule, and substitution of limits. It's below average difficulty as it involves only routine algebraic manipulation with no problem-solving insight needed. |
| Spec | 1.08b Integrate x^n: where n != -1 and sums1.08d Evaluate definite integrals: between limits |
| Answer | Marks | Guidance |
|---|---|---|
| \(\int_{-2}^{0} (9x^2 - 6x + 1) \, dx\) | M1 | |
| \([3x^3 - 3x^2 + x]_0^{-2}\) | M1 A1 | |
| \(= (0) - (-24 - 12 - 2) = 38\) | M1 A1 | (5 marks) |
$\int_{-2}^{0} (9x^2 - 6x + 1) \, dx$ | M1 |
$[3x^3 - 3x^2 + x]_0^{-2}$ | M1 A1 |
$= (0) - (-24 - 12 - 2) = 38$ | M1 A1 | (5 marks)\begin{enumerate}
\item Evaluate
\end{enumerate}
$$\int _ { - 2 } ^ { 0 } ( 3 x - 1 ) ^ { 2 } \mathrm {~d} x .$$
\hfill \mbox{\textit{Edexcel C2 Q1 [5]}}