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Math Help - Integration

  1. #1
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    Lightbulb Integration

    Hi,

    Is approximation the only way to solve Integral of e^(-x^2)/2 ?

    What if the integral is indefinite? Any suggestions?

    Thanks,
    Max
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  2. #2
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    I remember this integral being expressible in terms of pi.
    Last edited by wonderboy1953; September 3rd 2010 at 09:40 AM. Reason: correction
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  3. #3
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    The definite integral from 0 to infintity or from negative infinity to infinity is "expressible in terms of \pi".

    Whether "approximation the only way" depends upon what you mean by "approximation".

    \int_0^x e^{-t^2} dt= Erf(x).

    Would you consider \int_0^x \frac{dt}{1+ t^2}= arctan(x) only done by "approximation"? If not, how would you find arctan(x) for general x?
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  4. #4
    Senior Member AllanCuz's Avatar
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    Quote Originally Posted by wonderboy1953 View Post
    I remember this integral being expressible in terms of pi.
    You're thinking of the Gaussian integral: Gaussian integral - Wikipedia, the free encyclopedia

    To answer the OP, if the bounds are from negative infinity to infinity then the integral will become  \frac{ \sqrt{  \pi } }{2} . If, however, the bounds are finite the integral cannot be expressed in elementary functions: http://integrals.wolfram.com/index.jsp?expr=e^(-x^2)&random=false
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