I'm trying to integrate the Gaussian distribution between arbitrary limits, but I'm not having a lot of luck. As far as I can see I've done it right, but the answer I get is imaginary, which is obviously wrong, since it's supposed to represent a probability(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

a= 299

b= 301

β= -6.4e-6

α= sqrt(-β/π)

2. Relevant equations

http://img442.imageshack.us/img442/8195/croppercapture2jk3.png [Broken]

3. The attempt at a solution

Steps I'm taking:

- Turn it into a double integral over
xandy- Transform to polar coordinates; d
xdybecomesrdrdθand the limits become the corresponding values ofrandθforx=b,x=a(do I need to do something else with theθlimits perhaps?)- Evaluate the
r(inner) integral (with respect tor) and bring it outside the outer integral as a coefficient, since it's constant (is this part right? I'm not quite sure)- Evaluate the
θintegral; this just becomesθ(b) -θ(a).

Here's my working:

http://img208.imageshack.us/img208/5830/croppercapture6iq4.png [Broken]

Using this approach, I get an answer of 0.513e-5i, which is clearly wrong (it should be around 2.84e-3).

Can anyone tell me what I'm doing wrong? :(

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# Homework Help: Gaussian integration

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