does this problem make sense?

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November 24th 2008, 03:04 PM
RandomChampion

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
November 24th 2008, 03:43 PM
Plato

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.
November 24th 2008, 03:59 PM
RandomChampion

Quote:

Originally Posted by Plato

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