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Math Help - quick question about riemann sum

  1. #1
    Newbie RandomChampion's Avatar
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    quick question about riemann sum

    I would like to know if the integral of 16/(x^2) can be approximated using a Riemann sum. The integrals are from 0 to 2. I am asking this because at one of the boundaries, (0), f(0) is undefined (approaches infinity). However, i used n=4 and got an answer of 45.5556 as the Riemann sum. But shouldn't the area be infinite? I know Riemann sums don't give exact numbers and all, but if this is the case, can the Riemann sum be used when one of the boundaries is undefined?

    thanks for any help as i am completely confused right now
    Last edited by RandomChampion; November 24th 2008 at 08:05 PM.
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    You just can't do left Riemann sum (I guess you can and get infinity), but can still do the midpoint and right Riemann sum.
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  3. #3
    Newbie RandomChampion's Avatar
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    Quote Originally Posted by Linnus View Post
    You just can't do left Riemann sum (I guess you can and get infinity), but can still do the midpoint and right Riemann sum.
    great, thanks so much, so basically all i do is :

    f(.5)(.5) + f(1)(.5) + f(1.5)(.5) + f(2)(.5) = 45.5556
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    Quote Originally Posted by RandomChampion View Post
    great, thanks so much, so basically all i do is :

    f(.5)(.5) + f(1)(.5) + f(1.5)(.5) + f(2)(.5) = 45.5556
    A easier way would be .5 [f(.5)+f(1)+f(1.5)+f(2)], but yea, that would be how you do a right Riemann sum. Remember the answer you get will be nowhere near the correct answer.
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  5. #5
    Newbie RandomChampion's Avatar
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    Quote Originally Posted by Linnus View Post
    A easier way would be .5 [f(.5)+f(1)+f(1.5)+f(2)], but yea, that would be how you do a right Riemann sum. Remember the answer you get will be nowhere near the correct answer.
    yea i realize that, once again thanks a lot!
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  6. #6
    MHF Contributor Mathstud28's Avatar
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    Yes this integral is undefined, consider that

    16\int_0^2\frac{dx}{x^2}=16\lim_{\varphi\to{0}}\in  t_{\varphi}^2\frac{dx}{x^2} Now if you evaluate this integral keeping the limit in mind you will find it diverges to infinity.
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  7. #7
    Newbie RandomChampion's Avatar
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    Quote Originally Posted by Mathstud28 View Post
    Yes this integral is undefined, consider that

    16\int_0^2\frac{dx}{x^2}=16\lim_{\varphi\to{0}}\in  t_{\varphi}^2\frac{dx}{x^2} Now if you evaluate this integral keeping the limit in mind you will find it diverges to infinity.
    wait so does that mean i can't use a riemann sum on it?
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    Quote Originally Posted by RandomChampion View Post
    wait so does that mean i can't use a riemann sum on it?
    You can...but it's basically pointless since the answer is infinity. The right and midpoint Riemann will not give you a correct answer. It wouldn't even be really consider an estimate of the integral, which is one of the purpose of the Riemann sum.
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  9. #9
    Newbie RandomChampion's Avatar
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    Quote Originally Posted by Linnus View Post
    You can...but it's basically pointless since the answer is infinity. The right and midpoint Riemann will not give you a correct answer. It wouldn't even be really consider an estimate of the integral, which is one of the purpose of the Riemann sum.
    ok, sorry for being so confused. so me using the right riemann will not be incorrect, no matter how off the resulting estimate is?
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    Quote Originally Posted by RandomChampion View Post
    ok, sorry for being so confused. so me using the right riemann will not be incorrect, no matter how off the resulting estimate is?
    It depends on what the question is asking you to do. If it explicitly state "estimate the integral using the right Riemann sum with n=4 on the interval [0,2]" there isn't really much you can do.
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  11. #11
    Newbie RandomChampion's Avatar
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    Quote Originally Posted by Linnus View Post
    It depends on what the question is asking you to do. If it explicitly state "estimate the integral using the right Riemann sum with n=4 on the interval [0,2]" there isn't really much you can do.
    ok heres the exact question:

    Approximate the integral of 16/(x^2) dx using a Riemann sum with n=4, n=8

    so i gues there are three possible answers for each n value?
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    Quote Originally Posted by RandomChampion View Post
    ok heres the exact question:

    Approximate the integral of 16/(x^2) dx using a Riemann sum with n=4, n=8

    so i gues there are three possible answers for each n value?
    Yes, there are 3 possible answers for each n value.
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  13. #13
    Newbie RandomChampion's Avatar
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    Quote Originally Posted by Linnus View Post
    Yes, there are 3 possible answers for each n value.

    ok great, thanks a lot for all the help!
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