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November 16th, 2010, 09:02 PM   #1
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Approximation of an integral

My problem is to simplify the following integral:


I have a solution, but can't understand it without explanations. The solution is following:


, where , ,

The second case is clear: we expand the exponential term to the 2nd order Taylor series around u=1, simplify the expression, change variable, set the lower integration linit from 0 to and get the complimentary error function. But the first case result is not clear at all. Please, help me to understand. Thank you.
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November 17th, 2010, 01:10 PM   #2
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Re: Approximation of an integral

I won't try to answer your question, but I suggest trying a substitution x=u^2.
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November 18th, 2010, 12:05 AM   #3
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Re: Approximation of an integral

Thanx mathman, I finally solved it without substitution.
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