How can I find the following integral for $f(r) = r * e^{-r^2 K}$?

Question

There are a function $f(r)$. I would like to find the $\int\int_A f(r)drd\theta$

How can I find it? $f(r) = r * e^{-r^2 K}$

$K$ is just a variable.