Integral of e^(-x^2)

  • Thread starter imana41
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  • #1
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hi pleaes help me about this
[URL]http://latex.codecogs.com/gif.latex?\int_{1}^{\infty%20}e^{-x^2+2x}dx[/URL]

i know the [URL]http://latex.codecogs.com/gif.latex?\int_{0}^{\infty%20}e^{-x^2}dx[/URL] is [URL]http://latex.codecogs.com/gif.latex?\sqrt{%20pi}/2[/URL]
but can't solve above integral !?
 
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Answers and Replies

  • #2
Rewrite the power as:
[tex]
-x^{2}+2x=-(x-1)^2+1
[/tex]
It we define x-1=t,
[tex]
-x^{2}+2x=-t^2+1
[/tex]
so
[tex]
e^{-x^{2}+2x}=e^{-t^2+1}=e^{-t^2}e^{1}
[/tex]
and we also know that dx=dt, change the variable of integral and enjoy!
 
  • #3
36
0
thanks the the answer of integral is
gif.latex?\frac{e\times%20\sqrt{pi}}{2}.gif
 

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