Standard +0.8 This is a volumes of revolution question requiring rotation about the y-axis (less routine than x-axis), necessitating rearrangement to x in terms of y, finding intersection points, and careful setup of the integral. The algebraic manipulation and integration are straightforward once set up correctly, but the y-axis rotation and multi-step nature elevate it above average difficulty.
Fig. 6 shows the region enclosed by the curve \(y = (1 + 2x^2)^{\frac{1}{2}}\) and the line \(y = 2\).
\includegraphics{figure_6}
This region is rotated about the \(y\)-axis. Find the volume of revolution formed, giving your answer as a multiple of \(\pi\). [6]
Fig. 6 shows the region enclosed by the curve $y = (1 + 2x^2)^{\frac{1}{2}}$ and the line $y = 2$.
\includegraphics{figure_6}
This region is rotated about the $y$-axis. Find the volume of revolution formed, giving your answer as a multiple of $\pi$. [6]
\hfill \mbox{\textit{OCR MEI C4 2014 Q6 [6]}}