The error function, or erf, is defied as $${\rm erf}(x) = \frac{2}{\sqrt{\pi}} \int_0^x e^{-u^2} du .$$ The error function cannot be written in terms of elementary functions; this is the simplest way to write it.
Do a substitution, changing the limits of integration, to write the following integral as $a \, {\rm erf} (b x)$, where $a$ and $b$ are constants. Fill in the blanks with these constants.

$\displaystyle \int_{0}^{x} e^{-2 t^2} \, dt =$ ${\rm erf} ($ $x )$ .