Fresnel Integral Does someone know how they go from the left side to the right side?
$$\left(\int_{0}^{R}e^{-x^2/2}\,dx\right)^2 = \iint_{[0,R]^2} e^{-(x^2+y^2)/2}\,dx\,dy $$
Thanks.

Note that we can write 
$$\begin{align}
\int_0^R e^{-x^2/2}\,dx&=\sqrt{\int_0^R e^{-x^2/2}\,dx\,\int_0^R e^{-y^2/2}\,dy}\\\\
&=\sqrt{\int_0^R\int_0^R e^{-x^2/2}e^{-y^2/2}\,dx\,dy}\\\\
&=\sqrt{\int_0^R\int_0^R e^{-(x^2+y^2)/2}\,dx\,dy}
\end{align}$$
