Volume in cylindrical coordinates

[physics&math]

Homework Statement

Find the volume using cylindrical coordinates bounded by:

x²+y²+z²=2 and

z = x²+y²

Homework Equations

Converting to cylindrical coordinates:
z = √2-r² and

z = r²

The Attempt at a Solution

I figured z would go from r² to √2-r²
r from 0 to √2
and θ from 0 to 2∏.
However, when I evaluate the integral I get a negative volume. (And no, I did not forget to multiply by an extra r)

I have no idea where I've gone wrong.

 

[LCKurtz]

Homework Statement

Find the volume using cylindrical coordinates bounded by:

x²+y²+z²=2 and

z = x²+y²

Homework Equations

Converting to cylindrical coordinates:
z = √2-r² and

z = r²

The Attempt at a Solution

I figured z would go from r² to √2-r²
r from 0 to √2
and θ from 0 to 2∏.
However, when I evaluate the integral I get a negative volume. (And no, I did not forget to multiply by an extra r)

I have no idea where I've gone wrong.

What is the x,y equation of the intersection of your two surfaces? Are you sure you copied the problem correctly?