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June 6th, 2010, 12:36 PM  #1 
Newbie Joined: Jun 2010 Posts: 2 Thanks: 0  Help with limits for calculus homework
Evaluate the integral for n = 0, 1, 2, and 3. http://www.webassign.net/cgibin/symima ... 29%29%20dx I've already solved the one for n=0, it's 10. not sure how to exactly go about on the other ones. 
June 6th, 2010, 01:25 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,763 Thanks: 697  Re: Help with limits for calculus homework
Integration by parts can give you the integral involving x^n in terms of the integral involving x^(n1). Start with n=1 and work your way up.

June 6th, 2010, 01:45 PM  #3 
Newbie Joined: Jun 2010 Posts: 2 Thanks: 0  Re: Help with limits for calculus homework
I've tried. but I keep getting answers that don't make sense. I've taken the the integral from 0 to inf, and at n=1. I've let u=x, dv=e^x and so on. However, my answer is still wrong.

June 6th, 2010, 04:13 PM  #4 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,943 Thanks: 1132 Math Focus: Elementary mathematics and beyond  Re: Help with limits for calculus homework
I believe I have an answer for n = 1, if it's any help: Integration by parts: Let (We're doing a definite integral so I'll leave out the constant of integration). If my intuition is correct, to evaluate the definite integral we take the limit: For the limit rewrite as and apply L'Hopital's Rule, thus the limit is . So, I think my math is good  hope it helped. 
June 6th, 2010, 05:02 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,746 Thanks: 2133 
By the definition of the gamma function, If n is a nonnegative integer, that's 10(n!). I'll leave it to you to look up anything more you need (or use the method mathman suggested). Integration by parts: let etc. 
June 8th, 2010, 03:48 PM  #6  
Global Moderator Joined: May 2007 Posts: 6,763 Thanks: 697  Re: Quote:
, etc.  
June 9th, 2010, 04:53 PM  #7 
Newbie Joined: Jun 2010 Posts: 21 Thanks: 0  Re: Help with limits for calculus homework
You can make this a series so that you do not have to repeat the integral. So basically if you call Un=Integral(10*x^n*e^(x)) (n>0). You do the integral by parts of that and you will get Un=10X^(n)*e^(x) + nUn1 and Uo=10 like u already figured. And all you have to do now is plug in n for each number. Sorry I don't know how to put an integral here so hope u can read it.


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