| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indefinite & Definite Integrals |
| Type | Exponential and logarithmic integration |
| Difficulty | Moderate -0.8 This is a straightforward two-part question requiring basic algebraic expansion followed by routine integration of exponential functions. Part (i) is simple algebra, and part (ii) follows directly from the expansion with no problem-solving needed—just applying standard integration rules for e^x terms. |
| Spec | 1.06a Exponential function: a^x and e^x graphs and properties1.08c Integrate e^(kx), 1/x, sin(kx), cos(kx) |
| Answer | Marks | Guidance |
|---|---|---|
| \(e^{2x} + 2 + e^{-2x}\) | B1 | 1 mark |
| Answer | Marks | Guidance |
|---|---|---|
| \(\int(e^{2x} + 2 + e^{-2x})dx = \frac{1}{2}e^{2x} + 2x - \frac{1}{2}e^{-2x} + c\) | B1, B1, B1 | One for each exponential term, one for both \(2x\) and constant. 3 marks |
### (i)
$e^{2x} + 2 + e^{-2x}$ | B1 | 1 mark
### (ii)
$\int(e^{2x} + 2 + e^{-2x})dx = \frac{1}{2}e^{2x} + 2x - \frac{1}{2}e^{-2x} + c$ | B1, B1, B1 | One for each exponential term, one for both $2x$ and constant. 3 marks
---\begin{enumerate}[label=(\roman*)]
\item Expand $(e^x + e^{-x})^2$. [1]
\item Hence find $\int (e^x + e^{-x})^2 dx$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C3 Q2 [4]}}