Question

In Simpson's rule what does the x value represent in this section of the rule - 4f(xn-1) ?

Answer 1

I wish I had my old calc notes where I'm at now but this video should explain everything you need to know about simpsons rule:

https://www.youtube.com/watch?v=ns3k-Lz7qWU

Answer 2

I have watched this video many times, but I'll watch it once more to get to where I need to be in this question I'm facing. Thankyou.

Answer 3

It's just that there are many variations of Simpson's formula and I'm not sure which to use.

Answer 4

Give me a second I will explain to you
\[4f(x_{n-1})\]

well just say your n = 6

it would be your function with the 5th number subbed into it

Answer 5

are you sure there are multiple ways to do simpsons rule I thought it was just one formula

Answer 6

remember n = 6

so n -1 = 6-1 = 5

Answer 7

it is just notation because we cant be sure what n is so they say

n-1, n

Answer 8

when showing the general formula

Answer 9

it is the subscript that is confusing you right?

Answer 10

y = f(x)

so I think you are confused :S

Answer 11

If I'm wrong please correct me

Answer 12

Although, I guess you could derive other formulas, isn't simpson's rule the one with parabolas

Answer 13

The part that's confusing me is the x value in that part. not the subscript.

Answer 14

why is the x confusing you it is just f(x) with sub script n-1

Answer 15

you sub the function into it times it by 4 and sub the n-1 interval into the function

Answer 16

So if my n is 48.... n-1 would then be 47. I then sub my 47th value into the function and thats the value of the x in \[4f(x_{n-1})\]

Answer 17

wow 48 that is tedious lol

Answer 18

n equals the number of steps in an interval
what are you integrating between

Answer 19

Haha yeah you're telling me. I have figured all of the results for all 48 by subbing the intervals into the equation. I'm integrating between -1.7 and 3.1

Answer 20

graph appears as shown

Answer 21

Some calculus teachers are evil lol

Answer 22

yeah I know right... :c

Answer 23

trying to get wolfram alpha to split the interval up so lazy

Answer 24

so to find your intervals

figure out the distance from -1.7 to 3.1

so 1.7+3.1 = 4.8

4.8/48 = 0.1

so we just need to add 0.1 ugh

so

x_0, x_1,.....x_47, x_48
-1.7, -1.6,......3.0, 3.1

Answer 25

you can fill in whats inbetween

Answer 26

What is your function?

Answer 27

actually it doesn't matter.

In your case

\[4f(x_{n-1}) = 4f(3.0)\]

Answer 28

does that explain it?

Answer 29

the _ is to denote subscript btw

Answer 30

My entire function is (x-0.25)(x+1)^2(x-3)-5

Answer 31

do you follow??

Also, I can relate to your situation I once had an assignment where the prof wanted eulers method done with a period of like 30

Answer 32

so 4(((3)-0.25)((3)+1)^2((3)-3)-5)

Answer 33

but you wont see eulers method till calc 2

Answer 34

I do follow, in a round about way. It's just that I need to apply it to my situation.

Answer 35

The problem I had was that I got the right answer by just subbing the interval values into the function and then adding those 48 answers together.. i dont know why.

Answer 36

you dont understand the theory behind simpsons rule is that what you are getting at?

Answer 37

I'm sure you can find a video that provides proof but solving a simpson's rule problem is pretty systematic

Answer 38

Sort of. It's just confusing. idek anymore.

Answer 39

Well I recommend writing it down like you would a recipe for a cake

Answer 40

-first you write down the steps and the function
-then you write down the formula
-then you figure out the numbers in between the interval n
-then you sub everything into the formula

Answer 41

in this, what does \[2y_{n-1}\] represent?

Answer 42

by steps i mean n

Answer 43

You get
y = f(x)

right?

Answer 44

no

Answer 45

do you understand function notation?

Answer 46

lul no. i'm doing pre calc

Answer 47

like

you use to write (x,y)

now you write (x,f(x))

Answer 48

weird how precalc introduces simpsons rule :L I did it in calculus 1

Answer 49

Sorry I wasn't aware of what level you were at

Answer 50

it doesnt haha i just find it easier than trapezoidal

Answer 51

hmm
in Precal they are teaching Simpsons Rule ?
heard first time .

Answer 52

I like your school btw it is neat that they are teaching you this stuff.

we use f(x) instead of y because it allows us to talk about multiple functions without getting confused, the notation also lets us talk about specific points in the function without having to write out a value (which can save time).

For example,
y = 2+ x
becomes
f(x) = 2 + x
when we sub values into it
f(2) = 2 + 2
f(3) = 2 + 3

Answer 53

Haha they arent teaching me this I'm teaching myself thats why I need external help.

Answer 54

@Australopithecus I understand that stuff.

Answer 55

so what you are unable to understand ?

Answer 56

for example if we had two functions

y=2x + 2
y = 2x

we might get confused it is also a pain to write out the entire function when we wish to talk abut it so we give them notations

g(x) = 2x + 2
f(x) = 2x

now we can just say g(x) or f(x) when we wish to refer to the functions we can also talk about specific points in the function without computing them for example g(2) = 6, etc..

Answer 57

ok so you know that

f(x) = y

Answer 58

its the same thing thus it is equal

Answer 59

Yeah I guess so I've just never seen it in that form before.

Answer 60

the subscript n just talks about which interval you are subbing in

Answer 61

but I went over that so do you understand or are you still confused?

Answer 62

the f(x) and g(x) is used to find area between two functions though.
I'm just trying to find the area between the x axis and below of my graph shown

Answer 63

I know I'm supposed to use trapezoidal, but I don't like it so I'm teaching myself simpsons and I need some clarification on the steps. That is all.

Answer 64

where are you stuck

Answer 65

sorry repost your question and i will solve it now that i have your formula

Answer 66

I just need help using simpsons rule to solve the area below the x axis of my graph. that is all, please.

Answer 67

\[2y_{n−1} = (x_{n-1}-0.25)(x_{n-1}+1)^2(x_{n-1}-3)-5 = (3.0-0.25)(3.0+1)^2(3.0-3)-5\]

Answer 68

my function is (x-0.25)(x+1)^2(x-3)-5

Answer 69

there are 48 intervals of 0.1 between the x axis points of -1.7 and 3.1

Answer 70

right so you should do a number line

where -1.7 is x_0, -1.6, x_1... keep going to you hit 48

Answer 71

which should be 3.1

Answer 72

have done that already. subbed all the values between -1.7 and 3.1 into the function as well

Answer 73

got 48 results

Answer 74

where
a = -1.7
b = 3.1
n = 48 (number of intervals)

\[\frac{b-a}{n}(f(x_1) + 4f(x_2) + 2f(x_3) + 4f(x_4)........ 4f(x_{45}) + 2f(x_{46}+ 4f(x_{47} + f(x_{49}))\]

Answer 75

so if you have 48 numbers you add them all up and then multiply them by (b-a)/n

Answer 76

or 0.1

Answer 77

crud that should be x_0

Answer 78

not x_1

Answer 79

my formula is wrong I made a mistake in the subscript notation

Answer 80

but yeah simpsons rule is pretty straight forward just plug in the numbers into the formula, I can't really be anymore help than that video.

Answer 81

ugh I made a lot of mistakes explaining this to you but then again I'm pretty exhausted

Answer 82

That's okay I am too. It kind of makes more sense. This is just confusing though.

Answer 83

trust me it really isn't, it is very very simple there are no tricks to it it is really just plug things into the formula

Answer 84

OH MY GOD I JUST GOT THIS pellet.

Answer 85

good

Answer 86

You were probably over thinking

Answer 87

I totally was. omg. this is the most relieving day of my life..

Answer 88

I had it right all along it's just that my question had a scale of 10 so I had to multiply my answer by 10.
/le facepalm

Answer 89

this is what i got as the integral keep in mind they should be close but yours is more of an approximation (integrals use an n of infinity)

https://www.wolframalpha.com/input/?i=integrate+from+-1.7+to+3.1++%28%28x-0.25%29%28x%2B1%29^2%28x-3%29-5%29dx

Answer 90

That is the correct answer I just need to know how to figure that out by hand. ugh.

Answer 91

I don't know where you are getting stuck

Answer 92

You don't multiply f(x_0) or f(x_n) by anything everything inbetween gets multiplied by 4 then 2 then 4 then 2 then 4.... etc, you add all that pellet up and multiply it by 0.1 in your case

Answer 93

that is the best way I can describe the formula

Answer 94

it is just plug and chug it doesn't get any easier than that dont over think it