How can I get numerical answers to integrals involving the error function?

Question

This is the integral I am trying to evaluate in mathematica:

Integrate[Exp[-p^2/(m w h)], {p, -Infinity, Sqrt[h m w]}]

Can someone show me how to get a numerical answer out of this?

@belisarius I can if I copy and paste it into mathematica :D Is that not ok? — Logan, Oct 30 '14 at 04:40
@belisarius I wasn't sure how to write some of the stuff in latex. I'll look it up and re-type it though. — Logan, Oct 30 '14 at 04:47
Please, Oh Please! Until you master Mathematica: 1) don't use subscripts/superscripts and 2) Don't use Greek letters for posting here — Dr. belisarius, Oct 30 '14 at 04:53
Start reading this and then all the answers to that question — Dr. belisarius, Oct 30 '14 at 04:55
BTW, I see you've been around for about one year, but you don't vote too much and you usually don't accept answers to your questions. So, let me remind you: 1) When you see good questions and answers, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge. 2) Please remember to accept the answer, if any, that solves your problem, by clicking the checkmark sign! (On your past questions TOO!) — Dr. belisarius, Oct 30 '14 at 05:01

score 1 · Accepted Answer · answered Oct 30 '14 at 05:38

1

To get a numeric result you would need to assign numeric values to m, w, and h

int = Assuming[{Element[{m, w , h}, Reals], m w h > 0},
  Integrate[Exp[-p^2/(m w h)],
    {p, -Infinity, Sqrt[h m w]}] //
   Simplify]

1/2 Sqrt[[Pi]] Sqrt[h m w] (1 + Erf[1])

For example,

int /. {m -> 1., w -> 2. , h -> 2.}

3.2661

answered Oct 30 '14 at 05:38

Bob Hanlon

Thanks, that would make since. I was thinking the variables m and w would cancel out in the process because they are arbitrary in the problem I am working on but I figured it out. Thanks – Logan Oct 30 '14 at 05:58

1 Answers1