Let S be the region bounded on the interval 0≤x≤3 by the graphs of y=9−x2 and y=2x+3. This region is revolved about the x-axis.
(a) Explain, without performing any integration, why the volume generated cannot be represented by a single definite integral over the interval 0≤x≤3.
(b) Determine the x-value(s) at which the two bounding curves intersect and justify why these value(s) must be used to partition the domain.
(c) For each sub-interval identified in part (b), describe in words how the expressions for the outer and inner radii differ.