Simpson's Rule (1 Viewer)

[Riproot]

I'm doing it on Monday and would like it if someone could explain it, just so I can skip ahead, because I find my class is too slow and I skip ahead, get it wrong and then have to do it again sometimes...

 

[ohexploitable]

Simpson's rule approximates a curve into several parabolic sections and then sums up the areas of them. It is given by,

 

[Bored Of Fail 3]

just google it lol, I did find a good worksheet on it a few weeks a ago

it just works by apporximating the curve by a quadratic function, and then intergrating the quadratic function to get an estimate for the integral.

There is just one formula to remember and you should know that if you use simpsons rule to evaluate a definite integral of a quadratic function then you will get the exact value of the integral from using simpsons rule

 

[Bored Of Fail 3]

Simpson's rule approximates a curve into several parabolic sections and then sums up the areas of them. It is given by,

lol you actually memorse the formula, such a waste of time

 

[ohexploitable]

Since it approximates using parabolic arcs, Simpson's rule will give the exact result for quadratic functions (and cubics too I think but I'm not sure why).

 

[ohexploitable]

lol you actually memorse the formula, such a waste of time

I didn't intentionally memorise it, it's something that happens after doing many questions.

 

[Bored Of Fail 3]

^ you think it works for cubics

lol

 

[Riproot]

Simpson's rule approximates a curve into several parabolic sections and then sums up the areas of them. It is given by,

Thanks, I should be able to memorise this pretty easily.
I'm memorising the proofs for polynomials in MX2 at the moment, so this shouldn't be hard compared to that.

 

[cutemouse]

What about for more than 3 function values?

 

[Bored Of Fail 3]

What about for more than 3 function values?

i think you just give up and fail at that point

lol why memorise the case with three function values, if asked in an exam they will most likely ask for more than three function values, yes you could split it into 2 ( or more ) different regions and apply the formula ( what they do in general maths ) or you be smart and just always use the general formula

 

[ibbi00]

In a nut shell:
h/3 [1st + last + 2(odd) + 4(even)] where h = b-a/n
[y values. don't make the stupid mistake of putting x values here]

 

[Bored Of Fail 3]

In a nut shell:
don't make the stupid mistake of putting x values here]

y not lol, thats the best part

 

[ibbi00]

y not lol, thats the best part

Haha, done that way to many times. If my memory serves me well, you'll always end up with an answer of 0 and be like wtf???!!

 

[Bored Of Fail 3]

Haha, done that way to many times. If my memory serves me well, you'll always end up with an answer of 0 and be like wtf???!!

nah, but see I can see you have memorised it rather than understanding

what if the question was something like " use simpsons rule with 3 function values to estimate the area enclosed by the lines y=1, y=3 , x=0 and the curve y=e^-x"

hmm now in that case the area has been rotated so now you must use x values to get the correct answer.

see they need to start putting in these tricks to really test people, im sick of these tests where too many people can get 90/120 raw

I want to see people struggle to get 60/120 for a two unit paper, all the questions from 1-7 should be replaced with questions of Q8 difficulty

 

[ibbi00]

I'm pretty sure I came across such a question before. Wasn't that bad. But really, there's only so much you can recreate in maths. It will all end up being repetitive.

 

[ohexploitable]

see they need to start putting in these tricks to really test people, im sick of these tests where too many people can get 90/120 raw

The HSC is meant to test knowledge and how hard someone has been bothered to rote learn everything, it's not meant to test alertness and intelligence.

 

[Bored Of Fail 3]

The HSC is meant to test knowledge and how hard someone has been bothered to rote learn everything, it's not meant to test alertness and intelligence.

<<< is that you in the pic, I thought you were a guy

 

[ohexploitable]

<<< is that you in the pic, I thought you were a guy

Do you know many guys who do my subjects?

 

[Trebla]

I can post a derivation of Simpson's rule if you like (not the ones in Wikipedia), which uses concepts within the scope of this course.

 

[ohexploitable]

I can post a derivation of Simpson's rule if you like (not the ones in Wikipedia), which uses concepts within the scope of this course.

I'd like it

I haven't been taught this in class yet, I taught myself but unfortunately there's no derivation in my textbook :-(