Calc 3 - Double Integrals in Polar Coordinates

Hi there,

I'm absolutely drowning in my Calc 3 class and was hoping maybe someone here could explain things in terms that I understand. Naturally I've been pouring over my book and what-not, but there's one section that I just cannot seem to wrap my head around no matter how hard I try.

Here are some examples of problems:

1) Evaluate the following integral by changing to polar coordinates

$\displaystyle \int \int_{D} {x} {dA}$

where $\displaystyle D$ is the interval in the first quadrant that lies between the circles:

$\displaystyle x^2 + y^2 = 100$

$\displaystyle x^2 + y^2 = 10x$

2) Use a double integral to find the area of the region:

One loop of the rose: $\displaystyle r=9 \cos {3t}$

(the "t" should be a theta; can't figure out how to make it show correctly)

3) Use polar coordinates to find the volume of the given solid:

Above the cone

$\displaystyle z=\sqrt {x^2+y^2}$

And below the sphere

$\displaystyle x^2+y^2+z^2=13$

I don't expect anyone to solve these for me (in fact they are practice problems and I already have the answers) - I just want to know HOW to do them. I suspect the approaches to all three are very similar, but if I'm unwittingly asking too much here I would appreciate something like a link to a tutorial or something that could maybe help me.

Thanks for your time; any and all help is greatly appreciated :D