So, essentially you're integrating your function over the frustrum of an upside-down cone (frustrum in this context = cone with its head chopped off).
I would still use cylindrical coordinates (I think you meant to say cylindrical, not polar, though I grant you that cylindrical is just polar with an added cartesian coordinate).
I would split up your integral in two pieces depending on . Integrate on This would be the cylinder of radius from to . This corresponds to the "core" of the frustrum. Then, I would integrate on the outer cone part. Here, your limits would vary from to , your would vary from to , and you should be doing the integral, in that case, before the integral.
Can you put all this together and write down your integrals?