Fonction erreur

Surface comprise entre -y*σ et y*σ

Clear[y]

FullSimplify[Integrate[(1/(Sqrt[2π]σ)*Exp[-(x-μ)^2/(2σ^2)]),{x,μ-y*σ,μ+y*σ}, Assumptions -> {σ^2 ∈ Reals, σ > 0} ]]

N[%/.y->1]

Surface comprise entre -∞ et y*σ de la moyenne

Plot[Integrate[((E^(-((((x-μ))^2)/(2 (σ^2)))))/((Sqrt[2 π]) σ)),{x,-∞,μ+y σ},Assumptions->{(σ^2)∈Reals,σ>0}],{y,-4,4},BaseStyle->{FontFamily->"Times",FontSize->20},PlotRange->{Automatic,{0,1}}]

Plot[Erf[x],{x,0,3},PlotStyle->AbsoluteThickness[2]]

Simplify[(∫_(-∞)^x)((Exp[((-(x^2))/2)])/(Sqrt[2π]))\[DifferentialD]x]

Series[Erf[x],{x,0,4}]