Finding volume by rotating the region bounded by the given curves

Find the volume of the solid obtained by rotating the region (in both the first and second quadrants) bounded by the given curves about the specified axis.
http://math.webwork.rochester.edu:80...b69666e6c1.png about http://math.webwork.rochester.edu:80...81d03e5971.png

I got http://math.webwork.rochester.edu:80...eb93acf621.png but seems to be wrong...

This is how I would set it up...



This is basically integrating the area of a cross-section, which has . Then we see that the "radii" are given by (6 - f(x)) and (6 - g(x))
Where f and g are the given functions x^2 and 1.