given :

region R is x^2+y^2=2ax

we need to define the limit of R in terms of (r, theta) .

I got the answer from the book is 0< or = r < or = 2acostheta. I don't understand how this limit from. Could you please explain to me? Thank you very much.

For the theta limit is from -pi/2 to pi/2 . That is okay. I got this part.