| Exam Board | OCR MEI |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Volumes of Revolution |
| Type | Volume with exponential functions |
| Difficulty | Standard +0.3 This is a straightforward volumes of revolution question requiring the standard formula V = π∫y² dx with y = √(1 + e^(-2x)). The squaring eliminates the square root, giving a simple integral of (1 + e^(-2x)) which is routine to evaluate. It's slightly easier than average due to the algebraic simplification and standard exponential integration. |
| Spec | 4.08d Volumes of revolution: about x and y axes |
4 Fig. 4 shows a sketch of the region enclosed by the curve $\sqrt { 1 + \mathrm { e } ^ { - 2 x } }$, the $x$-axis, the $y$-axis and the line $x = 1$.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{88eadcf5-4335-4016-baf5-d3f74513bbb8-02_517_755_1576_649}
\captionsetup{labelformat=empty}
\caption{Fig. 4}
\end{center}
\end{figure}
Find the volume of the solid generated when this region is rotated through $360 ^ { \circ }$ about the $x$-axis. Give your answer in an exact form.
\hfill \mbox{\textit{OCR MEI C4 Q4 [5]}}