I'm doing some work - yes, on Thanksgiving

- 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) $\displaystyle y=sinx$, $\displaystyle y=0$, $\displaystyle x={2}\pi$, $\displaystyle x={3}\pi$; about the y-axis

2) $\displaystyle x=\sqrt{sin y}$, $\displaystyle 0 \leq y \leq \pi$, $\displaystyle x=0$; about $\displaystyle y=5$

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?

$\displaystyle \int_{{2}_\pi}^{{3}^\pi}2\pi{r}{h})dx$

So, I would take my $\displaystyle h = sin x$ and my $\displaystyle r = x$, giving me:

$\displaystyle \int_{{2}_\pi}^{{3}^\pi}2\pi({sin x})({x})dx$

Right?