Integrating a Vector Field Over a Circular Disk

[Phizyk]

Hi,
How do integrate this? I wish to see it step by step and I'm glad for any help i can get.
$$\int_{ \vec{r}\in{A}} \frac{ \vec{v}+ \vec{\omega}\times\vec{r}}{| \vec{v}+ \vec{\omega}\times\vec{r}|}d^{2}r$$
where A is area of disk with radius R.

 

[Matthaeus]

Can you explain some details? Where does the integral come from? Are v and omega constant for all r? Is omega perpendicular to the disk?

 

[Phizyk]

$$\omega$$ is the angular velocity of the disk, v is the translational velocity. v and $$\omega$$ are constants. Integration extends over the area of the disk with $$\vec{r}$$ vectors starting at the center.