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area under Gaussian curve

Keywords: 
double integral, polar coordinates
Synonym: 
Gaussian integral, area under the bell curve
Type of Math Object: 
Theorem
Major Section: 
Reference
Groups audience: 

Mathematics Subject Classification

26B15 no label found26A36 no label found

Comments

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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