Calculus - Shell Method to find volume

Hi,

Can you please help me and tell me if I got the right answers in these problems? :

http://i49.tinypic.com/2nsugr7.jpg

I just need the integral (I don't have to integrate).

Thank you in advance!

I think you did everything correct.

a)
y = x² + 1 <==> x = √(y - 1)
y(2) = x² + 1 = 5

length = 2π*radius = 2πy
height = 2 - x = 2 - √(y - 1)
thickness = Δy

from y = 1 to y = 5
V = ∫ 2πy(2 - √(y - 1) ) dy
or
V = ∫ 4πy - 2πy√(y - 1) dy

b)
length = 2π*radius = 2π(y - 1)
height = 2 - x = 2 - √(y - 1)
thickness = Δy

V = ∫ 2π(y - 1)(2 - √(y - 1) ) dy
or
V = ∫4πy - 4π + 2π√(y - 1) - 2πy√(y - 1) dy

c)
length = 2π*radius = 2πx
height = y - 1 = x²
thickness = Δx

from x = 0 to x = 2
V = ∫ 2πx(x²) dx
V = ∫ 2πx³ dx

d)
length = 2π*radius = 2π(4 - x)
height = y - 1 = x²
thickness = Δx

from x = 0 to x = 2
V = ∫ 2π(4 - x)(x²) dx
or
V = ∫ 8πx² - 2πx³ dx