I have the following problems:

(a) Evaluate $\displaystyle \int_{R^{3}} e^{{-(x^2+y^2+z^2)}}dV$

(b) Evaluate $\displaystyle \int_{R^{3}} e^{{-(x^2+2y^2+3z^2)}}dV$

I know how I am basically going to approach these (I am going to use spherical coordinates).

However, in other problems I was either given or could figure out the limits of $\displaystyle \theta$, $\displaystyle \phi$, and $\displaystyle \rho$. Here, I am at a loss. Any thoughts about what I should use for the limits of each of them?