okay, well umm, this last week we practiced ap tests and although it makes me sad to say, i think i did betteron the no calculator portion of the test than i did on the calculator allowed portion. but now is not the time for that, so i am just going to get this blog over with. for this blog i am going to write about riemann summs.
The first formula you need to know is x=(b-a)/n [a,b] with n subintervals. You will need to know this because each of the next formulas require that you know what x is.
LRAM- left hand approximation. (this puts the rectangles used to find the area on the left side of the curve) x[f(a)+f(a+x)+...f(b)]
RRAM- right hand approximation. (this puts the rectangles used to find the area on the right side of the curve) x[f(a+x)+...f(b)]
MRAM- approximation from the middle. (this puts the rectangles right on top of the curve, so that the curve goes through the middle of each one) x[f(mid)+f(mid)+...]
Trapezoidal- this does not use squares, instead it uses trapezoids to eliminate most of the empty space inside the curve, and I think this is the most accurate. x/2[f(a)+2f(a+x)+2f(a+2x)+...f(b)]
okay, well i know how to do all the stuff i mentioned above except for mram, so even though i have the formula i am not exactly sure how to do it. any help would be appreciated
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For mram, you take the midpoints of the numbers from lram, then you set up your formula like you are using lram, but with the midpoints you found.
ReplyDeletefind midpoints and then you just use the lram formula, except pluging in all the midpoints you found.
ReplyDeleteyou need all the midpoints from you lram then set up your formula teh same but use those midpoints that you found earlier
ReplyDeleteJust like everyone else stated you need to find your midpoints of the numbers that you use for your ram tests, then plug those numbers into your equation.
ReplyDeleteThe equation is ⌂x[f(mid)+f(mid)+...+f(mid)]
(⌂ is a delta)
say you have the intervals 1, 2, 3, and 4
to do MRaM you must find the number in the middle:
1,2 the middle number would be 1.5
2,3 the middle number would be 2.5
3,4 the middle number would be 3.5
For MRAM you need to find the midpoints that you used for the other riemann sums. Then you plug your midpoints into to equation
ReplyDeletedeltax[f(mid) + f(mid) + ... + f(mid)]