Simpsons/Trapezoidal? (1 Viewer)

[Popo Nana]

I can't find my 2U textbook, and there's usually ALWAYS a 2-5 mark question on these. Can anybody quickly post the formulae to use for these two methods?

I can tell I'm going to be reciting them frantically 20 seconds before the exam commences and writing them down as soon as Reading Time finishes v_v

~Popo

 

[Jago]

simpsons

(b-a)/6 [f(1) + 4f(2) + f(3)]

trap.

1/2 [f(1) + 2f(2) + 2f(3) + f(4)]

 

[lucyinthehole]

hey, if we don't use the formula, but the table method (anyone out there know what i'm talking about?) is that still valid?

 

[Popo Nana]

Thanks to both of you.

Lucy, I'm sorry, I really have no idea >_<

 

[PC]

The "table" method rocks! I swear by it! Totally valid and can be used for any question.

Example, use Simpson's Rule to approximate the area under the curve y = 2x - 5 for x = 1 to x = 5 with 4 strips (5 function values)

W = "weighting", P = procuct = W x f(x)

x f(x) W P
1 -3 1 -3
2 -1 4 -4
3 1 2 2
4 3 4 12
5 5 1 5
total = -3 + -4 + 2 + 12 + 5 = 12

Therefore Area = 1/3 x h x Sum = 1/3 x 1 x 12 = 4

Love the table method!

 

[bloodysunday]

i must admit i havent seen this method before - what does the 'weighting' mean?

 

[wind]

Easy way of remembering the rules:

Trapezoidal Rule:
h/2 [first + last + 2(remaining)]

Simpson's Rule (for 3 function values):
h/3 [first + last + 4(middle)]

Where h = (b-a)/2

They'll ALWAYS and ONLY ask for 3 function values. If not (and it's highly unlikely), just repeat the process for another 3 function values.

 

[PC]

In Trapezoidal Rule the formula is h/2 x [first + last + 2(rest)], so in the table method the weighting is 1 for the first, 1 for the last and 2 for the rest.

In Simpson's Rule the formula is h/3 x [first + last + 4(evens) + 2(odds)], so in the table method the weighting is 1 for the first, then 4, 2, 4, 2, ..., 4 and then 1 for the last.

So for the table method,
Trapezoidal Rule is 1/2 x h x sum
Simpson's Rule is 1/3 x h x sum
And h is just the difference between the values of x!

Sooooo easy!

 

[lucyinthehole]

i must admit i havent seen this method before - what does the 'weighting' mean?

wieghing is like the 4's and the 2's you put before function values in the formula, only condensed into a nice, neat table format