Evaluate the double integral ∬y^2/(x^2+y^2)dA, where R is the region that lies between the circles x^2+y^2=4 and x^2+y^2=81, by changing to polar coordinates.

In polar coordinates, the integrand should be r*sin(θ)/r² * r dr dθ, but I am unsure how to find the limits for r and θ. θ might be 0 to 2pi, and for the limits of r, I thought it might be like r^2=4 and r^2=81 so r goes from 2 to 9, but that isn't right.

Don't think I can explain it better than this.

https://www.youtube.com/watch?v=flaT7HuYk-Q

In polar, the integrand should be ( r*sin(θ))² /r² * r dr dθ, that turns out to be : r.sin² θ.dr.dθ.
Limits for r are 2 to 9, indeed.