Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.
y=x^2,x=y^2 about the axis x=–7
using discs (washers)
v = ∫[0,1] π(R^2-r^2) dy
where R = 7+√y and r = 7+y^2
v = π∫[0,1] (7+√y)^2 -(7+y^2)^2) dy
v = 149π/30
using shells
v = ∫[0,1] 2πrh dx
where r = 7+x and h = √x-x^2
v = 2π∫[0,1] (7+x)(√x-x^2) dx
v = 149π/30