Sketch the graphs of $y=\frac{2}{1+{{\left( x-2 \right)}^{2}}}$ and $y=1$ on the same diagram, showi

Question

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] Find the exact area of region $R$ enclosed by the two curves, the lines $x=1$ and $x=3$. [3] Find the volume generated when the region $R$ is rotated $360{}^\circ $ about the $y$-axis. [4]

Accepted Answer

(ii) $\pi-2\text{ units}^2$; (iii) $14.3\text{ units}^3$

2011 MI P2 Q2

2011 MI P2 Q2

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