Riemann's Sums

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Discus: SAT/ACT Tests and Test Preparation: May 2004 Archive: Riemann's Sums
By Skiowad (Skiowad) on Tuesday, May 04, 2004 - 07:22 pm: Edit

We never got to this stuff in our class (like a lot of other stuff). How important is it? The practice exams I saw only had one question about it or so. Is this right?

By Reeses (Reeses) on Tuesday, May 04, 2004 - 08:09 pm: Edit

I'm pretty sure there's always at least one question on it, and it's not too difficult to understand either...although I've forgotten what it is at the moment!

Can someone please explain it?

I know there's a left, right, and a middle...you have to add columns of numbers in the table...any help would be appreciated!

By Skiowad (Skiowad) on Tuesday, May 04, 2004 - 08:46 pm: Edit

same. a website or anything. thx I need all the help i can get. My class only got as far as area between 2 curves (actually i taught myself that and am about to see if i can teach myself the rest of calc. joy joy joy.) is the stuff after area between 2 curves hard? such as washer and disk method and slope fields thx

By Jlaws30 (Jlaws30) on Tuesday, May 04, 2004 - 08:51 pm: Edit

No, but the test is tomorow and volume will be on it. All you do is,
pi S(f(x))^2

pi x the integral of f(x) squared from a to b

By Aim78 (Aim78) on Tuesday, May 04, 2004 - 08:59 pm: Edit

It's just another name for LRAM, RRAM, and MRAM. If you don't know what that is, it's where you use rectangles to approximate the area under a curve.

By Skiowad (Skiowad) on Tuesday, May 04, 2004 - 09:08 pm: Edit

i know that!! My teacher sucks. A problem in our book was something like 1/n[(1/(1+1/n)) + (1/(2+2/n))...(1/(1+n/n)] Does anyone know what this is?!?! This sux

By Lifeisgood (Lifeisgood) on Tuesday, May 04, 2004 - 09:10 pm: Edit

Here's a go at explaining it... Reimann sums are basically the way that a lot of courses introduce integrals. The idea of a Reimann sum is to find the area under a curve by dividing it into rectangles and summing the areas of those rectangles. Here's an example. You know that fuel usage varies with time. You have a graph that is an exponential curve. You also have four data points: (0, 100), (1, 150), (2, 250), (3, 500). If you did not have an equation for that curve, one way to estimate to total amount of fuel used would be to form rectangles and add up the area of those. If you plot these ponits (hard to show online), you could make three rectangles. The length of each rectangle would be 1. The height is the y value at that point.

You have a few choices in which data points to use in finding the area. You could use the first three points. If you do so, you want to use the formula (b-a)/n * (y0 + y1 + y2). (a is the lower limit on the range, b is the upper, and n is the number of rectangles) As you can see, this will give you an underestimate of the value. Another option is to choose the final three data points. If you do so, you want to use the formula (b-a)/n * (y1 + y2 + y3). This method will give you an overestimate.

The third option to which you refer is to take the midpoint of each rectangle as the height of that rectangle. There, you would take the values at .5, 1.5, 2.5, etc. The formula for that is (b-a)/n * (y1/2 + y3/2 + y5/2). In most cases, the midpoint method will give you the most accurate estimate.

Reimann sums are related to integrals because, as you know, your estimate will get more and more accurate as the number of rectangles increases (and, therefore, as the thickness of each rectangle decreases). The integral is the limit as the thickness approaches 0.

Hope that helps!

By Skiowad (Skiowad) on Tuesday, May 04, 2004 - 09:18 pm: Edit

Does anyone know what I'm talking about?(I'm thinking mine is just an advanced problem of it. Is it?)

By Vinny919 (Vinny919) on Tuesday, May 04, 2004 - 09:27 pm: Edit

Skiowad, do you have the light blue calc book by ds marketing? Full of just 6 practice tests?

By Skiowad (Skiowad) on Tuesday, May 04, 2004 - 09:30 pm: Edit

yep, crap?

By Vinny919 (Vinny919) on Wednesday, May 05, 2004 - 10:23 pm: Edit

No, actually I found it very helpful, but then again I just got screwed on the FR today.

By Nycdebater (Nycdebater) on Wednesday, May 05, 2004 - 10:35 pm: Edit

omg riemann crap ..there was like 4 qusetions on the exam on that a long and its soo ez ..you should know it..but if u 4get how to do it..ur screwed..hey i was screwed..i 4got to multiple what wit what..like i knew how to do it..just not the formula..w/e..blah blah..i dont wanan think bout it

By Stonedpanda (Stonedpanda) on Wednesday, May 05, 2004 - 11:18 pm: Edit

hope you can do math better than you can write =p

rofl just playing =]~

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