Solution
= Solution
Since $X$ is nonnegative, $F_X(x)=0$ for $x<0$. For $x\geq0$, use $\frac{d}{dt}e^{-t^2/2}=-te^{-t^2/2}$ to obtain
$$
F_X(x)=\int_0^xte^{-t^2/2}\,dt=1-e^{-x^2/2}.
$$
Thus the <cumulative distribution function> is
$$
\boxed{F_X(x)=\begin{cases}0,&x<0,\\1-e^{-x^2/2},&x\geq0.\end{cases}}
$$
In particular it tends to one as $x\to\infty$, confirming normalization of this unit-scale <Rayleigh distribution>.