Reverse Integrals. (Check my work?)

I'm doing some work - yes, on Thanksgiving (Speechless) - and I've been doing good, but the paper reversed things on me! lol... I have to BUILD an integral, not solve it! Anywho, please check my work!

The problem(s) state(s):

Set up, but do not evaluate, for the volume of the solid obtained by rotating the region bounded by the given curves around the specified axis.

1) , , , ; about the y-axis

2) , , ; about

Okay, so for the first problem:

Looking at the graph and rotating it, I get a nice little donut. Since I need my approximating squares to touch BOTH functions, I have to use the Shell Method......right?

So, I would take my and my , giving me:

Right?

For the second problem, it's the same formula, but with and , giving me:

Thoughts?