How do I find the following volumes formed by rotating the region bounded by: y=x^2, x^2+y^2=2, about the line y=-2(set up only using dish or washer method)
The curves intersect at (-1,1) and (1,1)
So, using discs, and allowing for symmetry,
v = 2∫[0,1] π(R^2-r^2) dx
where
R = 2+√(2-x^2)
r = 2+x^2
using shells, and taking advantage of symmetry,
v = 2∫[0,1] 2πrh dy + 2∫[1,2] 2πrh dy
where r = y+2
and h starts out as √y and changes to √(2-y^2) when y=1