∫e^x^2dx=?
2012-02-14 12:14 am
圖片參考：http://imgcld.yimg.com/8/n/HA00016323/o/701202130044813873436730.jpg
http://i1099.photobucket.com/albums/g395/jasoncube/f0781511.png
回答 (8)
2012-02-15 6:57 am
✔ 最佳答案
圖片參考：http://i212.photobucket.com/albums/cc82/doraemonpaul/yahoo_knowledge/indefiniteintegral/integrateexpxsquare.jpg
參考資料：
my wisdom of maths
2012-02-15 5:31 am
The definite integral of it can be computed.
http://i187.photobucket.com/albums/x22/cshung/7008072400640.png
http://i187.photobucket.com/albums/x22/cshung/7008072400640.png
2012-02-15 5:18 am
This integral has no closed form. It is called the error function.
Simon YAU, MSc Math
Simon YAU, MSc Math
2012-02-14 5:24 pm
There is no simple function for this. This seems to be the ERF function. I have found the following: http://mathworld.wolfram.com/Erf.html
2012-02-14 5:08 pm
chu:
1/2x..x都唔係constant都比你放到出去
虧你話去考dse~幫人拉curve?
1/2x..x都唔係constant都比你放到出去
虧你話去考dse~幫人拉curve?
2012-02-14 8:49 am
You can use substitution.
Let u = x^2
du/dx = 2x
du = 2xdx
dx = du/2x
(Integrate) e^(x^2) dx
=(Integrate) e^u du/2x
=(1/2x) (Integrate) e^u du
=(1/2x) (e^u +c) where c is a constant
=(1/2x) (e^(x^2) + c)
Let u = x^2
du/dx = 2x
du = 2xdx
dx = du/2x
(Integrate) e^(x^2) dx
=(Integrate) e^u du/2x
=(1/2x) (Integrate) e^u du
=(1/2x) (e^u +c) where c is a constant
=(1/2x) (e^(x^2) + c)
參考: 2012 HKDSE M1 candidate
2012-02-14 5:11 am
Really??!!
2012-02-15 06:59:52 補充：
This kind of unproper integration problem is really interesting!!!
2012-02-15 06:59:52 補充：
This kind of unproper integration problem is really interesting!!!
2012-02-14 1:09 am
此積分無法以初等函數表示
收錄日期: 2021-04-13 18:32:21
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20120213000051KK00448