Find the volume of the solid obtained by revolving about the y-axis the region bounded by `y=2-(x^2)/(2), y=0, x=1, and x=2`
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Using the method of cylindrical shells, the volume of the solid obtained by rotating about the y-axis the region bounded by `y=2-x^2/2, y=0, x=1` and `x=2` is given by:
`rArr V=` `int_1^2 2pix(2-x^2/2)dx`
`rArr V=` `int_1^2 2pi(2x-x^3/2)dx`
Therefore, the volume of the required solid is `9/4pi` cubic units.
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