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Gaussian integral (view source)

Revision as of 02:18, August 17, 2015

4 bytes added ,  02:18, August 17, 2015
→‎Derivation: Wikify
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<math> = 2\pi \int_{0}^{\infty} e^{-r^2}rdr.</math>
 
<math> = 2\pi \int_{0}^{\infty} e^{-r^2}rdr.</math>
   −
Substituting <math>z=r^2</math> into the integral,
+
Substituting <math>z=r^2</math> into the [[integral]]:
    
<math> = 2\pi \int_{0}^{\infty} e^{-z}(z^{1/2})(\frac{dz}{2z^{1/2}})</math>
 
<math> = 2\pi \int_{0}^{\infty} e^{-z}(z^{1/2})(\frac{dz}{2z^{1/2}})</math>
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