\begin{align*}\displaystyle

\int_{\alpha}^{\beta}\int_{a}^{\infty}

g(r,\theta) \, rdr\theta

=\lim_{b \to \infty}

\int_{\alpha}^{\beta}\int_{a}^{b}g(r,\theta)rdrd\theta

\end{align*}

$\textit{Evaluate the Given}$

\begin{align*}\displaystyle

&=\iint\limits_{R} e^{-x^2-y^2} \, dA \\

(r,\theta) \, 2 \le r \le \infty \\

&\, 0 \le \theta \le \pi/2

\end{align*}$\textit{Rewrite with limits}$

\begin{align*}\displaystyle

&\lim_{b \to \infty}\int_{0}^{\pi/2}\int_2^{\infty} e^{-x^2-y^2} rdrd\theta

\end{align*}

just seeing if I'm going in the right directionâ˜•