Could anybody know formulation of integration

$\displaystyle f(x)=\int _0 ^x e^{-t^2}dt$

Formulation is not series.

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- Mar 18th 2009, 04:18 PMmath2009Error function
Could anybody know formulation of integration

$\displaystyle f(x)=\int _0 ^x e^{-t^2}dt$

Formulation is not series. - Mar 18th 2009, 06:01 PMmatheagle
you cannot integrate this, unless you let x go to infinity.

However you can approximate it via it's Taylor Series - Mar 18th 2009, 06:39 PMmath2009
I try to solve it, and get a approximate formulation

$\displaystyle \int _0 ^x e^{-t^2}dt \approx \frac{\sqrt{\pi (1-e^{-x^2})}}{2}$

There is small error when x < 3

I believe it must have precision formulation - Mar 18th 2009, 06:43 PMmr fantastic
It doesn't. Read this: Integration of Nonelementary Functions

- Mar 18th 2009, 07:06 PMmath2009
If k = 1.24 , then

$\displaystyle \int _0 ^x e^{-t^2}dt \approx \frac{\sqrt{\pi (1-e^{-kx^2})}}{2}$

It will approach very small error.

Could you find k or k(x) to minimum error ?

If we let limit of error to 0, it mean we get formulation

As your claim, "There are two things you should never try to prove ...... the impossible and the obvious."

You never prove it doesn't.