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June 6th, 2010, 12:36 PM   #1
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Help with limits for calculus homework

Evaluate the integral for n = 0, 1, 2, and 3.

http://www.webassign.net/cgi-bin/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.
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June 6th, 2010, 01:25 PM   #2
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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^(n-1). Start with n=1 and work your way up.
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June 6th, 2010, 01:45 PM   #3
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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.
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June 6th, 2010, 04:13 PM   #4
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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.
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June 6th, 2010, 05:02 PM   #5
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By the definition of the gamma function,
If n is a non-negative 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.
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June 8th, 2010, 03:48 PM   #6
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Re:

Quote:
Originally Posted by skipjack
By the definition of the gamma function,
If n is a non-negative 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.
Integration by parts:

, etc.
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June 9th, 2010, 04:53 PM   #7
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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) + nUn-1 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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