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simpsons rule wrong in excel text book? (1 Viewer)

1800-gumby

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I've been studying out of the excel step by step study guide and it has simpsons rule as h/3[(sum of ends) + 4(sum of odds) + 2(sum of evens)] my other text book i got from school (its a no name brand) gives it as h/3[(sum of ends) 2(sum of odds) + 4(sum of evens)]


Which ones right? i think the excel ones wrong but im not sure.
 
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Xayma

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If you have n function values then the even numbered ones, 2nd, 4th etc will be multiplied by 4.
 

JayWalker

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1800-gumby said:
I've been studying out of the excel step by step study guide and it has simpsons rule as h/3[(sum of ends) + 4(sum of odds) + 2(sum of evens)] my other text book i got from school (its a no name brand) gives it as h/3[(sum of ends) 2(sum of odds) + 4(sum of evens)]


Which ones right? i think the excel ones wrong but im not sure.
Yeah thats confused by most people. It depends if you do it like this..

Start with first function value as Fo then F1 F2 F3... Or
Start wiith function value as F1, then F2 F3

Depends if you start with your first function value as 1 or 0..

If you start as 0 then it is h/3[(Sum of Ends) + 4(Events) + 2(Odds)]
If you start with 1 then its h/3[(Sum of Ends) +4(Odds) + 2(Evens]

To avoid confusion, i just remember it as:

1 2 4 2 4 2 4 ... 2 4 2 1 (These are weightings)

Still confused then just start with F1 as your first and remember FOTE (Four Odds Two Evens)...

Understand?
 

1800-gumby

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ok thanx now i see where i've been going wrong i learnt starting with f0 then forgot the formula and used the one for f1.
Thanx again
 

smallcattle

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I dont understand what you guys are talking about...

i thought simpsons rule is (b-a)/6 * (F(a) + 4F((a+b)/2) + F(b)

whats h/3???
 

JayWalker

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smallcattle said:
I dont understand what you guys are talking about...

i thought simpsons rule is (b-a)/6 * (F(a) + 4F((a+b)/2) + F(b)

whats h/3???
HAHAAH.. yep, your screwed...

nah jokin
I think this is where you have gone wrong: Year 7 Maths... *joke* no really here is where i think your confused:

see you are only understanding Simpsons rule for a curve with only 3 function values

h = (b-a) / number of 'strips', hence with your curve, making h = 1/2, hence h/3 = 1/6.. actually i really have no clue..

someone please help her.. i have no idea WHERE she got (b-a)/6, but i know where her 4F((a+b)/2) came from, that would ONLY work with 3 function values. i.e the middle function value is avg of ends..

Good luck :uhhuh:
 

Xayma

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smallcattle said:
I dont understand what you guys are talking about...

i thought simpsons rule is (b-a)/6 * (F(a) + 4F((a+b)/2) + F(b)

whats h/3???
It is.

We use that same formula.

h=(b-a)/2, it just makes it more confusing.
 

smallcattle

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i am still confused.... so for example x=-1, -0,5, 0, 0.5, 1 using 5 values of simpsons rule

shouldnt i do (0-(-1)/6 * (f(-1) + 4f(-0.5) + f(0)) + (1-0)/6 * (f(0) + 4f(0.5) + f(1)) ????
 

Xayma

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it would be 1/6*(f(-1)+4f(-0.5)+f(0))+1/6*(f(0)+4f(0.5)+f(1))
=1/6(f(-1)+4(f(0.5)+f(-0.5))+2f(0)+f(1))
 

smallcattle

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its Q7 iv in the Independent paper 2004

but the answer showed as 1/2(f(-1) + 4(f(0.5)+f(-0.5)) +2f(0) + f(1))... thats why im confused
 

NeRdY

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It depends on how you have actually learnt it.

say you have:
F E O E L
X 1 2 3 4 5
Y -BLAH-

Where
F=first
E=even
O=odd
L=last

So then you apply this to the rule:

h/3{F + L + 4(even) + 2(odd) }

the way i always remember it you say:

"TODD" and "FLEA"

hope that helped! :p
 

DeadFish

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The universal one is:

h/3 [ f(A) + f(B) + 4*(first one after a) + 2*(the second) + 4* + 2* +...], where h is B-A/n. This should get you a corect answer every time. But even more importantly, you only have to use it once!

My opinions on the Simpson's Rule: This is very very poorly taught by the textbooks and teachers. Students get mixed up on virtually everything in this.

-with this equation, remember h as the width of one strip, NOT b-a/n
-don't bother with the odds evens crap. just remember it as a + b + then 4,2,4,2, starting from the first x-value after A to the value before b.
 
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