The antiderivative ofset equal to zero at x = 0 and multiplied by is called the error function, abbreviated erf x:
(a) Show that erf(±∞) = ±1.
(b) Evaluatein terms of erf x.
(c) Use the result of Problem to find an approximate expression for erf x when x ≫ 1.
Evaluate this integral approximately as follows. First, change variables to s = t2, to obtain a simple exponential times something proportional to s−1/2. The integral is dominated by the region near its lower limit, so it makes sense to expand s−1/2
a) The error function of x is given by
erf x = e-t^2 dt
erf x from 0 to is given by
erf x = e-x^2 dx