# Thread: Gaussian function -> Intergral = 1??

1. ## Gaussian function -> Intergral = 1??

I am struggling with this since hours!

the gaussian function is $g(x) = a*exp(-(x-b)^2/(2*c^2))$
This integral is 1 if and only if $a = 1/(c*sqrt(2*PI))$.
How is it possible then, that for example if c = 0.1, a = 1.0 / (0.1 * sqrt(2.0 * PI)) = 3.9894228.

I mean how can the integral be one, if g(0) is larger than one??

Any ideas what my mistake is here?

Thanks a lot!!!

2. ## Integral = Area

Suppose a rectangle is 2 units high and 1/2 unit wide. The area is 1.
If an integral is 1 (area under a curve), it could be a "narrow" curve, such as the one you have mentioned. Such a small value of c is an indication of this.