I'm trying my very best to understand it, but really, I just couldn't get it. I read four books now, and some 6 pdf files and they don't give me a clear cut answer :( Alright, so this integral; ∫e-x2dx from -∞ to ∞, when converted to polar integral, limits become from 0 to 2∏ for the outer integral, then 0 to ∞ for the inner integral. What I don't understand is, why is it if the original integral is ∫e-x2dx from 0 to ∞, the outer integral's limits become ∏/2? Why is it not ∏? Further, what if I need to integrate the same function, say from 0 to 1? Will polar integration help me? If it does, what will happen? Thanks and more power guys.