- #1

Inquisitus

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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

http://img442.imageshack.us/img442/8195/croppercapture2jk3.png

Steps I'm taking:

Here's my working:

http://img208.imageshack.us/img208/5830/croppercapture6iq4.png

Using this approach, I get an answer of 0.513e-5

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

## Homework Statement

*a*= 299*b*= 301*β*= -6.4e-6*α*= sqrt(-*β*/π)## Homework Equations

http://img442.imageshack.us/img442/8195/croppercapture2jk3.png

## The Attempt at a Solution

Steps I'm taking:

- Turn it into a double integral over
*x*and*y* - Transform to polar coordinates; d
*x*d*y*becomes*r*d*r*d*θ*and the limits become the corresponding values of*r*and*θ*for*x*=*b*,*x*=*a*(do I need to do something else with the*θ*limits perhaps?) - Evaluate the
*r*(inner) integral (with respect to*r*) 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
*θ*integral; this just becomes*θ*(*b*) -*θ*(*a*).

Here's my working:

http://img208.imageshack.us/img208/5830/croppercapture6iq4.png

Using this approach, I get an answer of 0.513e-5

*i*, which is clearly wrong (it should be around 2.84e-3).Can anyone tell me what I'm doing wrong? :(

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