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Math Help - does this problem make sense?

  1. #1
    Newbie RandomChampion's Avatar
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    does this problem make sense?

    Hi, i have a homework problem that is the following:

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

    then, the teacher sent an email to us saying that for this particular problem, "integral must be from 0 to 2", those were his exact words. i dont know if i am interpreting this, but if one of them is 0, doesnt that mean that this whole thing is DNE (can't divide by 0). if i am wrong, i still do not know what to do, as i'm sure that theres more than one kind of Reimann Sum (left, right and middle).

    any help is greatly appreciated
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  2. #2
    MHF Contributor

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    The real question here is “how does one partition the interval”?
    If n=4 & the interval is [0,2] then a partition is: [0,.5],[.5,1],[1,1.5],[1.5,2].
    That is known as a regular partition: each cell has length \frac{{2 - 0}}{4}.
    The fact is we can take any partition. But I think your instructor mean the regular one.
    Again, a Riemann sum can be formed using any set of points each selected from a different cell in the partition.
    So if I were you, I would use a regular partition and use whichever type sum you want, but be sure to explain which you are using.
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  3. #3
    Newbie RandomChampion's Avatar
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    Quote Originally Posted by Plato View Post
    The real question here is “how does one partition the interval”?
    If n=4 & the interval is [0,2] then a partition is: [0,.5],[.5,1],[1,1.5],[1.5,2].
    That is known as a regular partition: each cell has length \frac{{2 - 0}}{4}.
    The fact is we can take any partition. But I think your instructor mean the regular one.
    Again, a Riemann sum can be formed using any set of points each selected from a different cell in the partition.
    So if I were you, I would use a regular partition and use whichever type sum you want, but be sure to explain which you are using.

    so you are saying that I can use either the left, right, or middle method, because its not specified, but the instructor probably meant the middle method? i'm sorry if im misreading your post. also, i have a question about 0 being one of the endpoints. because 16/0 is undefined, doesn't that mean that the area/value will be infinite?

    thanks a lot for the help btw
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