posted by karlei .
Find the volume of the solid formed by revolving the region bounded by the graphs of y=3-(x^2) and y=2 about the line y=2
Why don't you translate the whole configuration down 2 units?
Then you would "find the volume of the solid formed by revolving the regions bounded by the graphs of y = 1 - x^2 and the y=2 (the x-axis) about the x-axis"
By the "Just-look-at-it Theorem" the x-intercepts are ±1 and there is symmetry, so you could just take it from 0 to 1 and double that.