Simpson's Rule (2 Viewers)

[del]

hmm i use y1 as first and remember it as

height/3 ( f(first) + f(last) +4f(evens) + 2f(odds))

 

[Angelic_Angel88]

Originally posted by Nightshade
Taking y0 as your first function:

h/3 [(first function + last function) + 4(all even values) + 2(all odd values)]

Thats it. Use nothing else.

Isn't it:
h/3 [(first function + last function) + 4(all odd values) + 2(all even values)] when taken y0 as your first function?

 

[smithy]

whoa whoa, hold on there- the way i remember it is by remembering the one with 3 function values
f(start) + 4f(middle) + f(end) so this means that the second value (which is even) is multiplied by 4, therefore the odd one is multiplied by 2- (since there are no odd values in 3 function values then there's no multiplication by 2)

 

[spice girl]

call the first function value f(0), the last function value f(2n), where there are 2n intervals each with width h

"wot weird letters...!?"

simpson's rule is:

V = (h/3)(f(0) + 4f(1) + 2f(2) + 4f(3) + 2f(4) + ... + 2f(2n-2) + 4f(2n-1) + f(2n))

 

[ProfesionalBull]

[(b-a)/6][f(a) + 4f((a+b)/2) + f(b)]

first post = ace

 

[Angelic_Angel88]

Aaack!

This whole thread has turned into one big confusing thread. LOL.

I say stick to whatever works best for you. And the formula that actually gives you the correct answer.

 

[elizabethy]

i think it is much better 2 use da table method..... rather than remembering these horrid formulas......

 

[Tritonair]

The rule as i have learnt it is

Two Odd Four Even (TOFFEE)

We have only just learnt this rule and i think that there is no way that you can beat integration, i mean the simple way, not this stupid simpson's rule and the trapezoidal rule except for questions like:

S1
X (x^-1)




:axedeath: (isn't this gif charming)

 

[sukiyaki]

i dun use the odd n even
i just grouped them in 3's and continuly add them

 

[tt_j65]

Originally posted by Nightshade
Peeps, the Simpson's Rule is easy. Taking y0 as your first function:

h/3 [(first function + last function) + 4(all even values) + 2(all odd values)]

Thats it. Use nothing else.

 

[Huy]

Originally posted by tt_j65

um ... it's the other way around

h/3 [y0 + yn + 4(y1 + y3 + ...) + 2(y2 + y4 +..._)]

Four the Odd, Two the Even
F.O.T.E.

you can use FLOE if you want, depends on which textbook you use, (first, last, odd, even)


Edit oops, i had just realised that people have corrected it already hehe... but yes, whatever works for you,

ACE? TOFFEE? that's new
i've always been a FOTE/FLOE person myself

 

[astron]

There is an easy way to clear this up.

Check your textbook. If you are using the one by Fitzpatrick (yellow cover), it is TOFE. Because they start with the first term being y1

If you use another text book (ie. the Coroneus ones, or the Excel books), its FOTE, because they start with a value of y0

It depends on what you're comfortable with, but try to use the one you've been taught IN SCHOOL, not at your tutor, because it is the school teachers who mark your tests.

 

[Winston]

i actually like the table method more better for some reason
the table method makes it easier for me

 

[Huy]

they normally give you the function values and interval widths.
so you should be okay,

if they don't, they'll give you enough information to work with and you'll be able to figure out the table of values from there (hopefully).

just remember to remain consistent.
if you're starting off with y1, y2, y3 ...

stick to it and know which formula/method you'd normally use,
otherwise,
stick with y0, y1, y2, y3 ... + yn

then use floe, fote, toffee, tofe, ace, whatever
just don't use the trapezoidal rule if it says simpsons

 

[iambored]

u may not need 2 know that exact rule, but u do need 2 know 1 that u learnt in class and obviously how 2 use it. there r many different variations.