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Changing the Gaussian Distribution from cartesian to polar coordinates

  1. Mar 27, 2013 #1
    1. The problem statement, all variables and given/known data
    "You are now going to show that, in the Gaussian distribution P(x)=Ae^(-Bx^2) the constant A is equal to sqrt(B/Pi). Do this by insisting that the sum over probabilities must equal unity, Integral(P(x)dx)=1. To make this difficult integral easier, frst square it then combine the integrands and turn the area integral, over x and y into an area integral over polar coordinates.


    3. The attempt at a solution
    The back of the book has this answer:
    1=A^2Integral(e^(-B(x^2+y^2)dxdy)=A^2Integral((e^-Br^2)(r)drdθ)=PiA^2/B.

    I understand the first piece but I don't understand how to get from these cartesian to polar coordinates at all, and I'm very confused as to how they got the final answer from the last integral.

    Please Help!
    Thanks!
     
  2. jcsd
  3. Mar 28, 2013 #2

    vela

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    You should review changing coordinates, which was covered in your calculus course.
     
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