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Gaussian Integral Substitution 
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#1
Feb1713, 03:07 AM

P: 8

If I had an integral
[tex] \int_{1}^{1}e^{x}dx [/tex] Then performing the substitution [itex] x=\frac{1}{t} [/itex] would give me [tex] \int_{1}^{1}e^\frac{1}{t}t^{2}dt [/tex] Which can't be right because the number in the integral is always negative. Is this substitution not correct? Sorry if I am being very thick but I can't figure out why I can't evaluate this simple integral with this change of variables. 


#2
Feb1713, 05:11 AM

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hi pcvrx560!
as x goes up from 1 to 1, t (= 1/x) goes down from 1 to ∞, and then from +∞ down to 1 … you'ld need to write ##\int_{1}^{\infty} + \int_{\infty}^{1}## (or ##\int^{1}_{\infty}  \int^{\infty}_{1}##) 


#3
Feb1713, 07:15 AM

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PF Gold
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Isn't the integral of e^x w.r.t. x simply e^x + C?



#4
Feb1713, 10:54 PM

P: 8

Gaussian Integral Substitution
Thanks, tinytim! That cleared it up for me.
I didn't think about the range I was integrating over, I was just mindlessly plugging numbers into 1/t. 


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