Transform an Integral bounds from -inf, inf to 0 to 1

Question

Good day,

If i have an integral from -infinity to infinity, how do I change the bounds/limits to 0 to 1? I don't want to give exact question since this is part of an assignment. I know how to figure out the integral but I am suppose to use Monte Carlo estimation.

Thanks

Answer 1

Look up logistic function.

Equivalently, hyperbolic tan (tanh) goes from $(-\infty, \infty) \to (-1, 1) $.

Then map to $(0, 1)$.