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[parent] area under Gaussian curve (Theorem)
AreaUnderTheBellCurve

"area under Gaussian curve" is owned by pahio. [ full author list (4) ]
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See Also: substitution notation, proof that normal distribution is a distribution, probability distribution function, error function, evaluating the gamma function at 1/2, normal random variable, table of probabilities of standard normal distribution, applying generating function

Other names:  Gaussian integral, area under the bell curve
Keywords:  double integral, polar coordinates

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generalisation of Gaussian integral (Derivation) by pahio
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Cross-references: even function, growth of exponential function, disc, double integral, limit, square, proof, curve, area
There are 9 references to this entry.

This is version 19 of area under Gaussian curve, born on 2005-05-17, modified 2008-08-15.
Object id is 7065, canonical name is AreaUnderGaussianCurve.
Accessed 20000 times total.

Classification:
AMS MSC: 26A36 (Real functions :: Functions of one variable :: Antidifferentiation)
 26B15 (Real functions :: Functions of several variables :: Integration: length, area, volume)
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request "integration" 2008-3-5 by pahio on 2008-03-05 12:17:38
itsiffi,
For convergence of the integral the coefficient (ia) of y^2 must be negative. It were clearer that instead of "ia" you write e.g. -a.
See the entry
http://planetmath.org/encyclopedia/AreaUnderGaussianCurve.html
Perform the substitution
y = t/\sqrt{a}, dy = dt/\sqrt{a}.
You will easily obtain the result \sqrt{\pi/a}.
Jussi
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