Re: integration to do with the error function...

In article <rbisrael.20070903001550$69ff@xxxxxxxxxxxxxxxx>,
Robert Israel <israel@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote:

The World Wide Wade <aderamey.addw@xxxxxxxxxxx> writes:

In article <1188715644.790559.95550@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
ycchen2000@xxxxxxxxx wrote:

I am using mathematica to calculate a nasty integration
to do with the error function, but to no avail.

It reads \int_a^b \sqrt{1-Erf[x]^2} d x with a and b any
number.

Can someone help? Originally, i intend to do a full integration from
negative infinite to positive infinite. But it won't work (returns the
same thing i typed in mathematica). Then i tryed finite integration,
again the same. Does anyone have any idea how to get the answer
of this integration ?

Note sqrt{1-Erf[x]^2} -> 1 as x -> -oo. This implies int_(-oo,oo)
sqrt{1-Erf[x]^2} dx = oo.

No, it goes to 0. The integral certainly converges.

However, int_(0,oo) sqrt{1-Erf[x]^2} dx converges.

Erf is an odd function, so sqrt(1-Erf[x]^2) is even. The integral
from -infty to infty is twice the integral from 0 to +infty.

Whoops, of course you're right. Some how I got it in my head that
Erf(x) is a constant times int_(-oo,x) e^(-t^2) dt. Never mind.
.

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