- #1

Kawakaze

- 144

- 0

I came across this in a textbook, it says its as good as impossible to integrate this expression. Ive met a lot of smart guys on here, maybe someone can do it?

[tex]\int exp (-x^2) dx[/tex]

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter Kawakaze
- Start date

- #1

Kawakaze

- 144

- 0

I came across this in a textbook, it says its as good as impossible to integrate this expression. Ive met a lot of smart guys on here, maybe someone can do it?

[tex]\int exp (-x^2) dx[/tex]

- #2

- 5,695

- 2,471

- #3

tiny-tim

Science Advisor

Homework Helper

- 25,838

- 255

Hi Kawakaze!

Sorry, the only way is to look it up in tables of erf(x) (the "error function") … see http://en.wikipedia.org/wiki/Error_function" [Broken]

(unless the limits are -∞ to ∞, or 0 to ±∞)

Sorry, the only way is to look it up in tables of erf(x) (the "error function") … see http://en.wikipedia.org/wiki/Error_function" [Broken]

(unless the limits are -∞ to ∞, or 0 to ±∞)

Last edited by a moderator:

- #4

Gib Z

Homework Helper

- 3,352

- 6

- #5

- 5,695

- 2,471

[tex]\int e^{-x^2}dx=\sum_{n=0}^{\infty}(-1)^n\frac{x^{2n+1}}{n!(2n+1)}+c[/tex]

- #6

Gib Z

Homework Helper

- 3,352

- 6

- #7

Phezboy

- 1

- 0

I

where y is just a dummy variable. Change to polar co-ordinates

r

dxdy=rdrdθ

I

which is trivial to calculate. You then take the square root of the answer.

- #8

- 22,178

- 3,305

I^{2}=∫e^{-x2}∫e^{-y2}

where y is just a dummy variable. Change to polar co-ordinates

r^{2}= x^{2}+y^{2}

dxdy=rdrdθ

I^{2}=∫∫re^{-r2}drdθ

which is trivial to calculate. You then take the square root of the answer.

Right. So you won't mind us giving us the value of

[tex]\int_0^1 e^{-x^2}dx[/tex]

if it is so trivial??

Share:

- Replies
- 5

- Views
- 1K

- Last Post

- Replies
- 2

- Views
- 342

- Replies
- 1

- Views
- 182

- Last Post

- Replies
- 3

- Views
- 194

- Last Post

- Replies
- 1

- Views
- 480

- Last Post

- Replies
- 4

- Views
- 269

- Last Post

- Replies
- 9

- Views
- 2K

- Last Post

- Replies
- 5

- Views
- 188

- Last Post

- Replies
- 4

- Views
- 136

- Last Post

- Replies
- 6

- Views
- 465