Integrate this integral from 0 to x of e^(-t^2)

[hytuoc]

someone please show me how to integrate this
integral from 0 to x of e^(-t^2)
Thanks

 

[Tide]

Your integral has no simple closed form. However, that particular integral appears often enough to warrant its own special designation - it's call the "error function:"

[tex]erf(x) = \frac {2}{\sqrt \pi} \int_0^{x} e^{-t^2} dt[/tex]

 

[quantitative]

Don't you square it. Rename a variable. Then transform to polar co-ords. Then you get left with something along the lines of...

I^2 = 2pi.int^x_0 r.e^(-r^2)dr

which is easy.

Think it's also called the guassian integral or probability integral and must be one of the most common integrals, comes up all the time in stats etc...

 

[Galileo]

Only when the limits of integration extend to infinity can we get a closed form expression by using that polar-coordinate trick.

What Tide means is that the antiderivative of [itex]e^{-x^2}[/itex] can't be expressed with elementary functions alone.