I get that. But when I integrate and plug in, I get the wrong answer. So I integrate sin(r) from r=2 to 6? that give me -cos(r) from r=2 to 6. Then, integrate -cos(2)+cos(6) from theta=0 to 2pi?
This gives me 8.647 which is incorrect.
The width of an infinitessimal element expressed in polar parameters is , and its length is . So the area of the infinitessimal element is:
That's where the 'extra' factor comes from.
As far integrating it, I don't have time to check it myself right now, but integration by parts might be the way to go.
I have a feeling your original integrand must have been , not seeing as it doesn't make sense to have mixed polars with cartesians in the first place. Also, doesn't have a closed form answer, whereas the first will.