what is integral of

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- Nov 29th 2011, 11:18 AMmoonnightingaleintegral of exp(-x^2)
what is integral of

- Nov 29th 2011, 01:20 PMTheEmptySetRe: integral of exp(-x^2)
does not have an elementry antiderivative. The integral can be calulated using Taylor series.

So we can integrate this term by term to get

This can be used to approximate the value to any accuracy you wish. The error bound is simple because the series is alternating. - Nov 30th 2011, 04:02 AMmoonnightingaleRe: integral of exp(-x^2)
- Nov 30th 2011, 04:16 AMHallsofIvyRe: integral of exp(-x^2)
What do

**you**mean by "manual method"? - Nov 30th 2011, 05:34 AMmoonnightingaleRe: integral of exp(-x^2)
i mean how to solve this by hand

by standard integration method - Nov 30th 2011, 05:35 AMmoonnightingaleRe: integral of exp(-x^2)
Kindly tell me how u will solve this integration question on paper

- Nov 30th 2011, 06:20 AMCaptainBlackRe: integral of exp(-x^2)
- Nov 30th 2011, 08:28 AMmoonnightingaleRe: integral of exp(-x^2)
can u tell me answer of my question

with simpson rule it comes to be

0.7455 - Nov 30th 2011, 08:49 AMHallsofIvyRe: integral of exp(-x^2)
You have been told twice now, by TheEmptySet and Captain Black, that [itex]e^{-x^2}[/tex] does not have an "elementary" anti-derivative.

If you insist upon such an answer then it is where "erf" is the Gauss error function. It is**defined**as . Does that help? - Nov 30th 2011, 08:53 AMOpalgRe: integral of exp(-x^2)
If you multiply it by , this integral becomes the error function, for which detailed tables of values are available (for example on the Wikipedia page that I just linked to). This gives erf(1) = 0.8427008. So your integral is that number times , or approximately 0.7468241.

- Nov 30th 2011, 09:16 AMAmerRe: integral of exp(-x^2)
cant we use that method suppose

then transfer to polar ?? - Nov 30th 2011, 09:19 AMTheEmptySetRe: integral of exp(-x^2)