Simpson's Rule & Numerical Integration

This calculus video tutorial provides a basic introduction into simpson's rule and numerical integration. It discusses how to estimate the value of the definite integral using simpson's rule. It also explains how to find the displacement of an object given a data table showing the instantaneous velocity of the object at different times. This lesson contains a few examples and practice problems for you to learn from.
Arc Length Problems:
• Arc Length Calculus Pr...
Surface Area Problems:
• Surface Area of Revolu...
Work Problems - Calculus:
• Work Problems - Calculus
Integration By Parts:
• Integration By Parts
Tabular Method:
• Integration By Parts -...
_______________________________
Trigonometric Integrals:
• Trigonometric Integrals
Trigonometric Substitution:
• Trigonometric Substitu...
Integration By Partial Fractions:
• Integration By Partial...
Trapezoidal Rule:
• Trapezoidal Rule
Simpson's Rule:
• Simpson's Rule & Numer...
________________________________
Improper Integrals:
• Improper Integrals - C...
Integration Into Inverse Trig:
• Integration into Inver...
Integration of Rational Functions:
• Integration of Rationa...
Integral of Logarithmic Functions:
• Integral of Logarithmi...
Integrating Exponential Functions:
• Integrating Exponentia...
__________________________________
Calculus Final Exam and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
/ collections

[@TheOrganicChemistryTutor]

Next Video: ruclips.net/video/ND9cEdfCFr0/видео.html
Final Exams and Video Playlists: www.video-tutor.net/

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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 RUclips TV with the Organic Chemistry Tutor.

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

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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

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[@STEMGeneralist]

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

[@mexicansombrero]

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

[@CosmeticYourWays]

It has to be given to you.

[@The_PES_Express]

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

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[@SW-2010]

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[@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

[@derpyherpy3773]

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

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Sight, me too...

[@Mpr91]

Thank you.

[@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.

[@foxtrot8325]

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)

[@ajgaming7167]

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

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[@alaminparves6926]

Answer?

[@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 ?

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[@AndyOseiAfrifa]

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

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thanks!

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Thank you

[@StephenJK1]

Thanks man

[@jeisongarrido7376]

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

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haha

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😂

[@MadaraAzukar]

Go ahead an try

[@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 :)

[@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

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[@Ru4444]

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

[@kaivenh]

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

[@Ru4444]

@@kaivenh 🤔 make sense, thanks! 👍

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You the best

[@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.

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Best ever seen

[@shashank_d_a]

Thanks Boss

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Simpson Rule is very good

[@NiiOswald]

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

[@butx1555]

n is the number of rectangles

[@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

[@salim___]

can u do laplace?

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[@theoreticalphysics3644]

Is there a way we can calculate error bounds?

[@CosmeticYourWays]

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

[@thrickercaster870]

do examples for fractions

[@ghosteen1890]

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

[@zaidradwan4000]

Thanx

[@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

[@rajorshikoyal4397]

Why are u taking n=4?

[@medotedo8410]

yES THAT IS BOTHERING try an odd one

[@ba4x594]

thx

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Nice

[@عبدالرحمنموني-ط9ث]

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

[@abradolflincler3257]

can i use any value as my n?

[@The_PES_Express]

Do this method with even number of data

[@filipps810]

how do we find X2i and X2i-1?

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[@gecaprathamesh6583]

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

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Why 2496?

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