Rotate a Circle Around the X/Y Axis - Cylindrical Shells

[sugarxsweet]

Homework Statement

Rotate the region bound by the given curve by about the x and y axis. Find the volume through the cylindrical method.
x^2 + (y-1)^2 = 1

Homework Equations

Cylindrical method: ∫2∏xf(x)dx
Slice Method: ∫A(x)dx

The Attempt at a Solution

x^2 + (y-1)^2 = 1
x = √(2y - y^2)

∫2∏x(√(1-x^2)+1)dx from -1 to 1
But this simplifies to 0... What am I doing wrong?

 

[sugarxsweet]

Help, please?

 

[HallsofIvy]

What do you mean by rotation "about the x and y axis". I know how to rotate around a single axis but not two.