Is this way of the Simpson and Trapezoidal rule correct for HSC or not? (1 Viewer)

[ckcalvin]

Can you use these methods in the HSC?


Simpson
A = h/3 [1st + last + 4(odds) + 2 (evens)]


Trapezoidal
A = h/2 [ 1st + Last + 2 (sum of others)]



or the stupid long way.

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

FOR TRAPEZOID
1/2 (b-a) f(a) + f(b)

 

[1titanic]

Hmm.. sorry that I don't answer your question
I do used that way your way or whatever lols
Are there other ways too?

 

[Lolsmith]

Stupid long way? Elaborate.

Generally, HSC markers will accept it if you make clear what you're substituting. If you don't utilise things outside of the 2U syllabus, they will usually give you the marks.

However, if you mean EXACTLY what you wrote there, they would mark it wrong. Last what? The last y term? x term? n term? You need to specify.

 

[ckcalvin]

Hmm.. sorry that I don't answer your question
I do used that way your way or whatever lols
Are there other ways too?

I am so confused cos this is the way everyone tells me to do it with but my teacher refuses to accept anything other than her long way. So i want to know the official way of doin this thing

 

[1titanic]

I am so confused cos this is the way everyone tells me to do it with but my teacher refuses to accept anything other than her long way. So i want to know the official way of doin this thing

Well obviously if the question asks you then you do what the question tells you to do
But what do you mean is it only finding area? because I only know that you use trapezoidal and simpsons rule to find area

 

[Trebla]

Can you use these methods in the HSC?


Simpson
A = h/3 [1st + last + 4(odds) + 2 (evens)]


Trapezoidal
A = h/2 [ 1st + Last + 2 (sum of others)]



or the stupid long way.

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

FOR TRAPEZOID
1/2 (b-a) f(a) + f(b)

They're the same thing, it's just the top formulae are extensions beyond two function values (i.e. multiple intervals) by adding each approximation found in the bottom formulae for the individual intervals which only look at two function values at a time.

For example, if you have two intervals say x = 0 to 1 and x = 1 to 2 to approximate an area under some function y = f(x), then by the trapezoidal rule for each interval (the bottom formula):

For interval 0 to 1:
(1/2)(1 - 0) [f(0) + f(1)] = (1/2) [f(0) + f(1)]

For interval 1 to 2:
(1/2)(2 - 1) [f(1) + f(2)] = (1/2) [f(1) + f(2)]

Adding the two individual approximations gives:
(1/2)[f(0) + f(2) + 2f(1)]

which takes the form of the top formula for trapezoidal rule

 

[ckcalvin]

Well obviously if the question asks you then you do what the question tells you to do
But what do you mean is it only finding area? because I only know that you use trapezoidal and simpsons rule to find area

well obviously these are rules to find approximation of areas -.-

 

[1titanic]

well obviously these are rules to find approximation of areas -.-

no I mean.. oh wait now the long way appears
I was asking do you mean anything else rather than that

 

[bouncing]

hmm good quesiton
i used the first 2 (since they are SOOOO much easier to remember) in my halfyearliers, and there wasnt a problem? im not sure tho maybe its just the way my teachers mark...

really the 2nd way is just a harder way of saying the first.... dont see the point of remembering it :\ besides if u want to confuse urself (Y)

 

[Lolsmith]

Are the ways I write it.

 

[ckcalvin]

They're the same thing, it's just the top formulae are extensions beyond two function values (i.e. multiple intervals) by adding each approximation found in the bottom formulae for the individual intervals which only look at two function values at a time.

For example, if you have two intervals say x = 0 to 1 and x = 1 to 2 to approximate an area under some function y = f(x), then by the trapezoidal rule for each interval (the bottom formula):

For interval 0 to 1:
(1/2)(1 - 0) [f(0) + f(1)] = (1/2) [f(0) + f(1)]

For interval 1 to 2:
(1/2)(2 - 1) [f(1) + f(2)] = (1/2) [f(1) + f(2)]

Adding the two individual approximations gives:
(1/2)[f(0) + f(2) + 2f(1)]

which takes the form of the top formula for trapezoidal rule

So if i were to write this formula properly in an exam how would i write it??

 

[ckcalvin]

Are the ways I write it.

thanks bro i'll take your word. Now i just have to pray my teacher won't give me zero.

 

[Trebla]

So if i were to write this formula properly in an exam how would i write it??

The formal way to write the trapezoidal rule under multiple applications (which is the summation of the single applications) for example is:



and for Simpson's rule under multiple applications it would be:



For single applications the trapezoidal would be:



and for Simpson's rule it would be:



Don't bother trying to quote the formulae "properly" because it's too long and will probably just confuse you. Just plug the numbers in as I've shown above. It doesn't matter which approach you take. They're both correct.

If your teacher strictly stipulates a certain method then you must follow that method because he/she is the one marking it. However, in the external HSC exams it doesn't matter which approach you take.

 

[DNETTZ]

Can you use these methods in the HSC?


Simpson
A = h/3 [1st + last + 4(odds) + 2 (evens)]


Trapezoidal
A = h/2 [ 1st + Last + 2 (sum of others)]



or the stupid long way.

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

FOR TRAPEZOID
1/2 (b-a) f(a) + f(b)

Yes, its right, and I use them too.
They're from the extension section of the Cambridge book, as I recall?

 

[Affinity]

Pretty sure you just need to write down the line with the substitution CORRECTLY.