2011 MI P2 Q2
(i)
Sketch the graphs of $y=\frac{2}{1+{{\left( x-2 \right)}^{2}}}$ and $y=1$ on the same diagram, showing clearly the coordinates of the stationary point and points of intersection between the curves.
[2]
(ii)
Find the exact area of region $R$ enclosed by the two curves, the lines $x=1$ and $x=3$.
[3]
(iii)
Find the volume generated when the region $R$ is rotated $360{}^\circ $ about the $y$-axis.
[4]
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