Integralen av $$$e^{- a^{2}}$$$

Bestäm $$$\int e^{- a^{2}}\, da$$$.

Denna integral (Felintegral) har ingen sluten form:

$${\color{red}{\int{e^{- a^{2}} d a}}} = {\color{red}{\left(\frac{\sqrt{\pi} \operatorname{erf}{\left(a \right)}}{2}\right)}}$$

Alltså,

$$\int{e^{- a^{2}} d a} = \frac{\sqrt{\pi} \operatorname{erf}{\left(a \right)}}{2}$$

Lägg till integrationskonstanten:

$$\int{e^{- a^{2}} d a} = \frac{\sqrt{\pi} \operatorname{erf}{\left(a \right)}}{2}+C$$

$$$\int e^{- a^{2}}\, da = \frac{\sqrt{\pi} \operatorname{erf}{\left(a \right)}}{2} + C$$$A