Simpson's Rule & Numerical Integration

[@TheOrganicChemistryTutor]

Application of Integration - Free Formula Sheet: bit.ly/3ZdKSnK Integration Techniques - Video Lessons: www.video-tutor.net/integration-techniques.html

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[@AbwaEric-j4d]

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[@georgesadler7830]

Professor Organic Chemistry Tutor, thank you for a solid analysis of Simpson's Rule and its impact on Numerical Integration in Calculus. Simpson's Rule is the best approximation that can be used to approximate Definite Integrals which can/cannot be Integrated in closed form in Calculus. This is an error free video/lecture on KZbin TV with the Organic Chemistry Tutor.

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... nerd

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Never studied calculus before, but I have a module on numerical methods at college. This has helped a bunch. Thanks.

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The example is a useful one. Never did I imagine that calculus can actually be applied in real life!

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Very useful! thanks for uploading, also would be cool if you had video on Calculating Theoretical Maximum Truncation Error

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Thank you for another awesome video. Now let's have a moment for the word mess up at 5:03.

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"so that's it for this particular problem" - what did he mess up on?

[@Exorcist-z3z]

​@@tannerkayla1076"2500 divided by 4 is 2496"​

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Great explanation!

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[@harshbirbrar2830]

What happened to the fx n-2, fx n-1? You never elaborated on what the means or when that's used nevermind: it just meant 3rd last term, 2nd last term, and fx n would be last term

[@RockyReynolds-h1m]

When you did the definite integral as you got to the very end you said "twenty five hundred divided by four". @4:30

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thanks!

[@SW-2010]

Thank you sir.

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[@ajgaming7167]

why did you use n=4 when calculating deltaX do you just pick any number or I'm confused

[@ajgaming7167]

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[@alaminparves6926]

Answer?

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[@StephenJK1]

Thanks man

[@youtubesubtitles9741]

Why is n equal to 4? 01:30

[@youtubesubtitles9741]

@@404luxx I figured it out later that day, anyway thank you

[@Octeeve]

Just because

[@derpyherpy3773]

In my book, △x = (b-a)/(2*m). Where does that formula come from? I can't find it anywhere else.

[@jamestanny849]

Sight, me too...

[@The_PES_Express]

If n is even then what will happen 4*f(xn-2)

[@jerenaki1834]

You the best

[@mexicansombrero]

How do you determine the n value (number of rectangles)?

[@CosmeticYourWays]

It has to be given to you.

[@wysonnkhalango1302]

Where were you getting that denominator 3 in both first examples? I have not understood that part

[@davidalli6683]

It's part of the formula

[@Alejandro14300]

Thank you.

[@abdul-muizhammed4377]

God bless you and your family

[@antoniusdaivaprabawisesa6686]

but what if the n is odd? does the middle part of the sequence end with 2.f(Xn-1)?

[@abdus684]

Simpson's method doesn't work for odd n .. you have to use trapezoidal method if you would like t use n s odd :)

[@sitaro98]

What happens if you choose to work with four points? What coefficient will the two middle term have?

[@lukewilkerson3574]

Simpson's rule only works for N = even integer. so go back to Trapezoidal rule for N = odd integer. The reason we use Simpson's over the trapezoidal is it is more accurate.

[@autumn_auburn]

Sorry for the late answer. To apply Simpson's rule, you need to divide the interval I even number of parts(eg 2,4,6 etc) Even number of parts implies odd number of points, for example- We divide the interval [0,2] in four parts, then there are four sub intervals- [ 0 , 0.5 ] , [ 0.5 , 1 ] , [ 1 , 1.5 ] , [ 1.5 , 2 ] But number of points = 5 (i.e. 0, 0.5, 1, 1.5,2)

[@hozaifaradwan9343]

Thank you

[@ChancyNeatwell]

Best ever seen

[@shashank_d_a]

Thanks Boss

[@muhammadidrees3701]

If maximum value of double derivative is zero in Trapezoidal Rule ( for example if f(x) = x sinx [0 , pi ] ) then how do you find error ?

[@jeisongarrido7376]

You forgot to say "In this video..."

[@kairumaina5266]

haha

[@rawshthussain2875]

😂

[@MadaraAzukar]

Go ahead an try

[@davidking7712]

Thanks

[@stalinmatos3296]

How did you you get 6 intervals from 0 to 30 how is 05 one interval and than 5 to 10 is another one. but then 10 to 25 is the third, are these uneven intervals? might be a silly question but it caught my attention for some reason. thanks again.

[@harshbirbrar2830]

where did you get 10-25 is the third from? 0-5: 1st 5-10: 2nd 10-15: 3rd 15-20: 4th 20-25: 5th 25-30: 6th

[@STEMGeneralist]

The second velocity problem. Both solutions are considered equal since the ones ans decimal are not significan figures.

[@abdulrahmanradwan6167]

Simpson Rule is very good

[@salim___]

can u do laplace?

[@ghosteen1890]

thanks man

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How do I give you money for your service lmao

[@Marcosss-7-years-ago]

3:25 some asmr type shit😂

[@AndyOseiAfrifa]

Both trapezoidal and mid ordinate rules gave me 50700. It looks like the interval is huge or.....

[@lunditv]

Nice

[@theoreticalphysics3644]

Is there a way we can calculate error bounds?

[@CosmeticYourWays]

Yes, it is normally the next section in your calc class.

[@abradolflincler3257]

can i use any value as my n?

[@moeberry8226]

Couldn’t you add up all the velocities and then divide by 7 since the distance is equal to the displacement in this case. I think you get a small margin of error because of the simpsons rule.

[@Attalla-t9b]

THANKSSSS

[@NiiOswald]

it should be 51300m instead of the 50600, great work though

[@Ru4444]

Why use simpson's rule when u can just use definate interal to solve it? 😳 and why did u call "n" a rectangle?

[@kebbean]

i’m not sure but maybe because computers can solve it

[@Ru4444]

@@kebbean 🤔 make sense, thanks! 👍

[@andonttd]

Love you

[@zaidradwan4000]

Thanx

[@thrickercaster870]

do examples for fractions

[@ba4x594]

thx

[@butx1555]

n is the number of rectangles

[@matthewkoob7600]

What a god

[@MRAXELGRINDER]

great

[@The_PES_Express]

Do this method with even number of data

[@filipps810]

how do we find X2i and X2i-1?

[@rajorshikoyal4397]

Why are u taking n=4?

[@medotedo8410]

yES THAT IS BOTHERING try an odd one

[@kaneruumguysdoprettymuchan4379]

I have one problem how the hell do you know this many subjects it like you have a PHD in everything

[@aimanhakimadenan9781]

Why different N value give different answer?

[@ASOUE]

The more rectangles you have, the smaller they must be to fit in a given space. If you use more, smaller rectangles, they answer is naturally going to be more accurate, because there is less excess, and the rectangles are getting closer and closer to a single line that fits perfectly under the curve.

[@aimanhakimadenan9781]

@@ASOUE thank you

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You saved me!

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[@zaidradwan4000]

nice

[@Fffffffffffffffgggg]

You have made a mistake .. it is (delta x over n-1 ) not over n

[@yawdery3359]

is this the 1/3 rule or 3/8

[@ursulasvetlana742]

1/3

[@gecaprathamesh6583]

It was not coincidence in first question…Simpsons rule gives exact answer even for cubic polynomials! If anyone knows how please tell me

[@friedhegg8874]

lol what

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[@johnairamislangclar6097]

Why 2496?

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Thanks

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Thank you.