transformation of integral from 0 to infinity to 0 to 1 How do I transform the integral $$\int_0^\infty e^{-x^2} dx$$ from 0 to $\infty$ to o to 1 and. I have to devise a monte carlo algorithm to solve this further, so any advise would be of great help

This is a pretty weird integral. There is no elementary antiderivative for $e^{-x^2}$. However, the area under the entire curve is $\sqrt{\pi}$. The details escape me at the moment, but you can derive this be rotating the curve around the y axis, changing to polar, then integrating. So, if
$$\int_{-\infty}^\infty e^{-x^2} = \sqrt{\pi}$$
what happens when the lower bound is $0$?
