aha.. and now people are supposed to help you? In which way is it dependent on r? So r changed from 1 to 10000. is r the integration limit then? I thought there were no integration limits.
Please tell us about your background. Do you have any idea how integrating in principle works?
Is not enough for you a statistical estimate like: alpha ≈ a•\[{R}^{b}\] ?
with "a" and "b" are constants depending from frequency (and temperature) and R is the rain rate.
However you can find all the details in the book: "Satellite Communications Systems Engineering" by L.J. Ippolito