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Does anybody have any idea about this one?

thanks guys

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- Thread starter grant369
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- #1

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Does anybody have any idea about this one?

thanks guys

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To use an infinite number of strips to estimate the area, you must first realize that taking the integral of a function is taking the sum of the area of each strip from i=1 to infinity, where i is the strip. Does that make sense so far?

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i think i follow

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Gib Z

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[tex]\int^{10}_2 x^2 dx = \frac{10^3}{3} - \frac{2^3}{3}[/tex] In case your wondering.

How ever, the way the question is stated, i think you have to do it this way:

Use a model of riemann sums, say..left hand sums. Make an equation using the sums that calculates the area for a given number of the rectangles. Then take the limit of the number of rectangles to infinity.

- #5

HallsofIvy

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That's very poorly stated. A Riemann sum does NOT have an "infinite number of strips". Any Riemann sum has a finite number of strips- the integral is then the limit as the numbeer of strips goes to infinity. I suspect what is expected is a formula for the Riemann sum for "n" strips, then calculate the limit as n goes to infinity.

Does anybody have any idea about this one?

thanks guys

Actually, there exist an infinite number of

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sorry if im being vague..

- #7

HallsofIvy

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I'm sure all this is covered in your text book- review. Also, because this is clearly homework, I am moving this thread to the homework section.

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Thankyou

P.S. if anyone has any ideas about the strengths and limitations of this model compared with other models such as the trapezoidal rule, monte carlo, definte integral etc that would also be of great assistance

- #9

Gib Z

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Search Lebsegue integral for a better one.

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Gib Z

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thanks

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Gib Z

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- #13

HallsofIvy

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But that's not the point of Riemann sums. Riemann sums are used as a way to

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Gib Z

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Gib Z

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sorry gib z...i was actually referring to Halls of Ivy...i should have quoted him. Sorry

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Gib Z

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Its ok don't be sorry lol.

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HallsofIvy

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thanks

It's still not clear to me what your question is! Are you talking about strengths and weaknesses of methods of deciding how to set up an integral or for doing a numerical integral?

If you are talking about doing a numerical calculation of an integral, while a "Riemann sum" (I wouldn't call it that) using rectangles is simpler for each individual piece, Simpson's rule is so much more accurate for the same amount of calculation that I wouldn't consider using anything else.

If you are talking about deciding how to set up an integral for a specific application, simplicity is everything and "accuracy" (since you will be doing the same integral in the end) I would only consider Riemann sums.

The problem I have is that I don't consider "Riemann sums" as anything like the "trapezoid rule" or "Simpson's rule"- they are intended for completely different things.

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what about compared to the monte carlo method of integration

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