2018 MI P2 Q1
In the diagram, the region $R$ is bounded by the curves $y=-{{x}^{2}}+3x-1$, $y=\sqrt{x}$ and the $y$-axis.
Without using a graphing calculator, find the volume of the solid generated when $R$ is rotated through $2\pi $ radians about the
$y$-axis.
[4]
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