Step-by-step explanation:
The integral was obtained using cylindrical shells. The volume of each shell is:
dV = 2π r h t
where r is the radius, h is the height, and t is the thickness.
The thickness is either dx or dy. Looking at the integral, we can tell it is dy. So the solid is revolved about the x-axis (or a line parallel to the x-axis).
The radius will be y. So the height must be x = 9/(9+y²).
So the solid is obtained by rotating the region 0 ≤ x ≤ 9/(9+y²), 0 ≤ y ≤ 3 about the x-axis.
