# [SciPy-User] solving integration, density function

Tue Dec 21 05:06:50 CST 2010

```Hello,

I am really new to python and Scipy.
I want to solve a integrated function with a python script
and I think Scipy should do that :)

I do have some variables (s, m, K,) which are now absolutely set, but in future I'll get the values via another process of pyhton.

s = 400
m = 0
K = 1

And have have following function:
(1/((s*K)*sqrt(2*pi)))*exp((-1/2*(((x-m)/s*K))^2) which is the density function of the normal distribution a symetrical curve with the mean (m) of 0.

The total area under the curve is 1 (100%) which is for an integration from -inf to +inf.
I want to know x in the case of 99%: meaning that the integral (-x to +x) of the function is 0.99. Due to the symetry of the curve you can also set the integral from 0 to +x equal to (0.99/2):

0.99 = integral((1/((s*K)*sqrt(2*pi)))*exp((-1/2*(((x-m)/s*K))^2)), -x, x)
resp.
(0.99/2) = integral((1/((s*K)*sqrt(2*pi)))*exp((-1/2*(((x-m)/s*K))^2)), 0, x)

How can I solve that question in Scipy/python
so that I get x in the end. I don't know how to write
the code...

thank you very much

johannes
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