Problem 6P

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.

Problem:

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

Solution

Step 1

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