Polar coordinate limits for Definite integral of $\int_{a}^{\infty}t^2e^{t^2}$ dt

Question

Can anyone help me with this integral $$I = \int_{a}^{\infty}t^2e^{-t^2} dt$$ $$I^2 = \int_{a}^{\infty}\int_{a}^{\infty}t^2h^2e^{-t^2-h^2} dt dh$$ Can you please explain how I can find the limits in the polar coordinates for the above integral? I am trying to do this similar to the way we evaluate the integral of Gauss distribution.