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November 16th, 2010, 09:02 PM  #1 
Newbie Joined: Nov 2010 Posts: 2 Thanks: 0  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. 
November 17th, 2010, 01:10 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,807 Thanks: 717  Re: Approximation of an integral
I won't try to answer your question, but I suggest trying a substitution x=u^2.

November 18th, 2010, 12:05 AM  #3 
Newbie Joined: Nov 2010 Posts: 2 Thanks: 0  Re: Approximation of an integral
Thanx mathman, I finally solved it without substitution.


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approximation, integral 
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