Q on Trapezoidal rule (1 Viewer)

[bails]

Im really confused, coz i dropped down from 3U to 2U my teacher taught us how to do the trap rule as:

= (b-a)/2 [f(a) + f(b)]

instead of the other way, & seeing i never learnt the other way, can anyone explain it to me or should i keep using this way?

 

[Viper]

Well.... to start with , it it aint broke, dont fix it...

I do 3 unit, and i use heaps of 3 unit principles in 2 unit... I really dont think they can mark you down, as you are demonstrating extended mathematical knowledge....

Personally, i use:

A = (h/2)[(yo+yn)+2(y1+y2+y3+.....+yn-1)] and h=(b-a)/n

This is the general formula, and will work in ANY trapezoidel question. This probably the one they showed you in 3 unit??

(oh yeah... the n is the number of sun-intervals)

Goodluck

Cheers

 

[slyball]

this is my explanation:
(b-a)/2 [f(a) + f(b)] is the general trapezoidal rule - but it has a large error ratio (doesn't take into account the curvature).

h/2[f(a) + f(b) + 2f(the rest of the functions)] ... where h = (b - a)/n is the trapezoidal rule which takes into account subdivisions (ie. the strips), thus resulting in a more accurate version of the general formula.

hmmm.. hope you understand. it's kind of confusing to type.
if they ask you a question to do with the trapezoidal rule, you can use either formula, but if they ask a question to use trapezoidal rule with x amount of sub-intervals, then you have to use the second one.

edit: viper beat me.

 

[bails]

Like i could learn that method, coz then i wouldnt hav to do it so many times, but could u explain that way to me in english plz, coz i dont get it just from reading the text book =)

 

[Viper]

Im not sure what you want explained....

How the formula works?
How to apply the formula?

Cheers

 

[bails]

umm... how to apply the formula, like if a q has 6 function values, where do the intervals go, whats the y's stand for? Sorry i think im confusin myself.

Whats this thing about evens and odds? hmm mayb i should stick to the longer way cin its like 2 days away!

 

[Viper]

Ok... umm... ill see if i can' explain...

6 function values means that there are 5 sub-intervals. If you dont remember this from class, just draw yourself up a simple graph and mark 6 points on the x-axis (any six points will do... you could try every half centimetre or something). Now, draw a vertical line from each of those lines so they touch the graph you drew. These lines are your funtion values. The 'sub-intervals' are the 'strips' in between these lines. you will observe that there are 5 sub-intervals

The general rule is the the number of sub-intervals is the (number of function values) - 1.

This works for both the trap rule and Simpsons.

The 'y's are the function values (as marked by 'slyball'). The function values are the y-value at that x-value.

Ill try to explain...

y=x^2

where: x=1, y=1
x=2, y=4
x=3, y=9
x=4, y=16

The x-values are the points you marked on your graph before (on the x-axis)... the y-values are the points at which the vertical lines touch the graph you drew.

so, when i put the 'y's in the formula, i am substituting the x-values into the equation of the graph.

I really hope this makes sense...

Tell me if it doesn't

Cheers

 

[slyball]

Originally posted by bails

Whats this thing about evens and odds? hmm mayb i should stick to the longer way cin its like 2 days away!

the evens and odds are part of simpson's rule..

 

[bails]

Ahhhhhhhhh, that makes sense! Righton so the no. of function values will always be b on the squiggly line thingy.

Right, i think its all down pact, just one more q.

For [y0 +2(y1+y2+...+Yn-1) + yn)

yo=the first sub interval
then the ones in the brackets are say to till 5 ( for the 6 sub interval q) and
yn= the 6th sub interval?

 

[bails]

Originally posted by slyball
the evens and odds are part of simpson's rule..

Right thanx, man i so dont get this chapter..hopefully by mon i will thanx to Viper's help! Peace

 

[Viper]

Yeah bails, that sounds good.

No worries, good luck

Cheers

 

[bails]

Righton, thanx for all ya help! Good luck to u 2!