Problem with integrals

Hello, I find it hard to understand the regions of integral when solving multivariable integrations, such as in double integration. I would like to discuss and learn about strategies and methods on how to go through the process of facilitating knowledge about the region/interval of the ​​integration. Would you like to share your thought process when you solving a double integral in polar coordinates? for example: Regards /Anhard

f is a function defined in R: f(x)=x ;if x ϵ Q f(x)= 0;if x ∉ Q PROOF THAT lim f(x) = 0 when x --> 0