Simpsons Rule - Approximate Integration

[colebluefearn]

Thanks for making this video. Very clear and helpful. Cheers!

[swethajan]

Nice video!!! would be great if you can come up with the proof too!!many people quit the proof if it's there in the text book, but incase you can come up with a such a video, I bet there would be any skipping!!:D

[beto3k]

What if the value at X0 ends up in division by 0? It happened in a hmk problem and I wasnt sure what to do

[Shanongao]

Why is it multiplied by 4 and 2?? He doesn't explain where 4&2 came from

[patrickJMT]

@Shanongao no, i do not derive the formula. the derivation / proof is in any calculus textbook.

[Shanongao]

@patrickJMT ty! my bad i should have at least looked into my text book before conplaining srry and thnx again for ur wonderful and insightful vids patrick!

[patrickJMT]

@Shanongao no worries ;) i would like to start doing proofs/justifications of the theorems. it seems more people would like to see those than what i originally thought. i always just assume 99% of people skip over them (which probably is true)

[indiabharatsachin]

very very good explanation

[mcdovis2009]

Jonny la gante esta muy loca!? WTF!?

[milkykungnaja]

Thanks for sharing a nice collection of your videos. Easy to follow and well-explained ^_^ Just subscribed. Please keep it up.

[insectoidizm]

have u heard of a calculator

[fuzzballjunior2]

This makes the book seem like it's written in Yiddish....

[rpgmakr]

This is just wonderful. After trying to understand cryptic explanations on the internet this video actually showed me how this is done. Thank you!

[spacedakini]

Thank you, very nice and clear!

But how is the formula derived? Thats what I was actually looking for...

[patrickJMT]

@spacedakini check your textbook, they show in there : )

[spacedakini]

@patrickJMT

Which textbook?



[spacedakini]

I only have a confusing script from my teacher, full of typing errors (!)...

[rockguyjw]

calculator method (using graphing calculator of course):

1) plug in integrand into Y1

2) Got to Stat, Edit

3) Into L1 plug in the sequence in this case from 0 to 3 at a .5 interval (this can be done by going to 2nd List OPS seq. Then it's seq (x,x,0,3,.5)

(This is the number that he drew out, but on the calculator instead)

4) Plug into L2: Y1(L1) (Y1 can be found in Vars -> Y-Vars -> Function) (L1 is 2nd 1).This evaluates the integrand at each of the values of the number line) See next comment

[rockguyjw]

@rockguyjw 5)Plug in 1,4,2,4,2,4,1 into L3 manually. These are the co-efficients of 4's and 2's

6)Plug into L4: L2*L3. This multiplies the coefficients of 4's and 2's by their respective values

7) Got to main screen, then do sum(L4) (sum is 2nd -> List -> MATH)

8) That's your answer :D Basically what he did but on the calculator

Thanks again man for the great video

[rockguyjw]

can you derive simpson's rule? I'm the kind of guy that doesn't like using formulas/calculator unless I know where it comes from, why it works and when to use it.

[shaider1982]

How did I get from Simpsons to Simpson's rule?;) Seriously, this method has been used by ship designers for a long time.

[junglecrane]

where delta x is the length of the integral divided by uern

[notnever5]

@IsraelJosefowitz when we cannot evaluate the integral so we make an approximation. its just another method of numerical integration which is often used in computational programming. There are also cases when simpson's rule is the same as the integral. but the main applications i have learned about is when you cant find the integral through integration or you would like a computer program to find an approximation, since computers cant simply compute an integral with basic programming.

[notnever5]

thanks! very easy to follow and concise.

[amjanna12]

Omgoodness, you have saved my life. My calculus teacher is AWFUL, and this usually clears up all of my questions I have. Thank you!

[deejaycea101]

CALC 2!!! i'm doing this in calc 1, FML!!!

[amjanna12]

@deejaycea101  Me too. Isn't it just so fun? :P.

[samy9387]

no hating 

[DerickisG]

i <3 yooooou

[ohwowashley31]

my teacher expects me do to that calculation with out a calculator. It's great.

[Jiopaba]

Wow. This is beyond fabulous. It's amazing how many fabulous videos you can find on YouTube explaining math. I can sit in class for a full hour listening to the teacher talk about it and see her do fifteen different examples and not have a goddamned clue. But I go home, look at the homework problem, see what it asks, and type into YouTube "How to approximate area under curve via Simpson's Rule." I don't even have to get a quarter of the way through the video before it makes perfect sense.

[11airheads]

i am so happy that i found this video two days before the test :D

thanks!!

[ImYours4Ev]

I wish I found all of these before the night before my test! These are very helpful! :)

[XenomexTutorials]

It's easier to do 4x(ODDS)+2x(EVENS)

Great video nonetheless.

[11solrac44]

thank you very much for making these videos they really help. I'm studying for my calculus test and the video really helped.

[imtrill07]

is this the same as simpson's 1/3?

[Dexxomify]

@imtrill07 Yes 1/3 h is the same thing

[Cdtms92]

Thanks man! Making my day a little easier haha!

[Jenksssss]

On some of my questions it says "using x ordinates" instead of "using x intervals/integrals", is this the same thing? Thanks..

[tdr124]

So when evaluating the function on the inside part the scalars on the endpoints are just one and the inside just alternates between 2 and 4? okay doesn't look so bad now. I think.

[tagseeker]

thanx buddy it helps alottttttttttttttttttttttttttt­tttttttttttttt

[patrickJMT]

@ferasteddy calculator

[PmQable1]

couldnt you factor that to 1/(x^4+i)(x-i) and use partial fractions to finish integrating? please correct me if im wrong.

[ian559fresno]

@patrickJMT Thanks :D

[ian559fresno]

Thanks for all your videos...I have one question...what is integration used for? Like I know how to use it but what does it do? Like if we try to find the tangent line we take the derivative etc...what does this do?

[patrickJMT]

@ian559fresno to find the net change

[jayleon07]

@ian559fresno Integration finds the area under a curve (if that's what you mean.)

[ian559fresno]

@jayleon07 thanks :)

[kcorpetti14]

@ian559fresno The deritave of a function gives us the rate of change of an exact moment in the function, .o they can be used to understand how a function works without having the graph, Integration is the reverse process. In Electricity, finding the area under the curve of a graph of Current vs Time gives you Voltage. Its applications are endless.

[Rapol12]

squeeze and tedious are your favorite words.

[MagnaCarta0]

I thought that you divide the N value by 3, not the delta X value?

[OpenTheTrollGate]

is the simpson's rule a way to approximate a definite integral???

I noticed that the simpson's rule equation is not equal to the equation for the definite integral.

[OpenTheTrollGate]

where does the rule come from?

[NSpire2BVC]

for school i have to do this for f(x) = -x^2-8x-7 with n=12.....this gunna take a long time!!!! D:

[raschdieek]

Much love for the videos. My Calc book doesn't have any good examples. This helped a ton!

[sussa05]

It would be interesting if you also had calculated the error we commit with this method. Great vid though! Cheers!

[FiaskoHD]

1/6[(first+last terms)+4(odds)+2(evens)]

[jennybon999]

than youuuu you just made calculus so much easier!!!!

[TheAngryL3B]

you sir are a legend!

[kissroby123]

what is n=? in my problem n it`s not given

[tub214hi]

YOU ARE GOD. please tell me you make money doing this somewhere...

[zombiecrowtv]

my books makes simpson's rule look like a monster and you make it look like a cute little puppy.

[Jess123369]

isnt simpson's rule also (2(Midpoint rule) + trapezoid rule)/3?

[tessb]

@fazz26 its an arbitrary choice. generally, the smaller the n, the smaller the pieces, the more accurate your answer. usually on a exam, your teacher will give you an n for consistency in answers. in the real world, you can determine what your error would be based on your n and then you would choose it yourself so you have the least amount of calculations (bigger n, more calculations) and the greatest amount of accuracy necessary.

[Avatar230594]

You saved me

[mohamedezeldin]

you are amazing thank you very much

and please add more...

[Marzipancandy]

I LOVE YOU PATRICK! I FINALLY LEARNED THIS WITH YOUR HELP!

[fazz26]

this video relly explianed everything....but why did u use n=6....?

[SaintsRow740]

THANK YOU SO MUCH. I WAS HAVING TROUBLE UNDERSTANDING THIS AND IT WAS ANNOYING ME, BUT SINCE I WATCHED THIS I UNDERSTAND IT ENOUGH TO FINISH MY ASSIGNMENT. CAPITAL LETTERS!!!!

[MegaPullareddy]

you've really helped me a lot ..i still wanted to listen from you about the errors in trapezoidal rule

[HughJass125]

I have to do this in highschool calc...

[iancar29]

Very neat and easy to go by , cheers!

[MRH3LO]

Thank you very much, helped me HEAPS :)

[HadiJ89]

Question: Is simpson's rule solely used when asked? [ given (n) ] Would it ever occur in which (n) is not given? Also, what are the best ways to establish that we do need to use simpson's rule?

[patrickJMT]

@HadiJ89 it is just a way to approximate an integral. you can use it whenever you want. most problems you would see on a test would ask you to use it. typically n will also be specified.

[TheBull06]

@patrickJMT I thought simpson's rule was only used when n is even

[Gofflyman]

@HadiJ89 If 'n' is not given just make up your own knowing that that greater number of strips (n) the more accurate the area can be calculated. The catch; more strips(n) = more work. Integration uses near infinite number of strips. When to use it? When your told to genrally, but If you were given a bunch of data containing a bunch of y values and you don't know what the function is, then you could use Simpsons rule to find the area under the curve.

[hawxboy1]

Thanks so much this has saved my life u r brilliant

[jayross3]

Thanks for the vids keep em coming.

[NappySupreme]

just curious as to why there is integration in the notation when there seems to be no actual integration happening? great vid btw.

[patrickJMT]

@NappySupreme well, we are approximating the value of that integral in a round about way (which is why there is no actual integration)

[RossMathTutoring]

@NappySupreme The beauty of the midpoint formula, trapezoidal rule, simpsons... is that if you have an INTEGRAL that is too difficult or even impossible to solve (i.e. e^-x^2) then you can just plug in the formulas and VIOLA'! You have yourself a fine approximation.

[ryingling5711]

Why does the equation alternate 4's and 2's?

[patrickJMT]

@ryingling5711 short answer: you would have to read the proof

[MrJigab00]

@patrickJMT could u please expand what u mean by read the proof

[patrickJMT]

@MrJigab00 well, most people watching calculus videos have a calculus book, so the proof/justification of the formula would be in the book. i am sure you could also just google something like : proof simpson's rule calculus, and you could easily find something on the net about it.

[Naytah]

You, sir, are a rock star.

[arzgania]

dude thanks so much..I actually came to this link looking for a reason as to why I couldn't set up my S.R right..turned out I inverted the 4,2 coefficient series.. /facepalm

again thanks!

[arzgania]

I love the clarity of the marker! Its the little things that really, really help!

[winfi103]

is 0/0: 1, 0, or undefined

[10CEDENOMI]

YOU ARE MY SAVIOR!!!...YOUR MAKING MY DREAMS COME TRUE MAN!

[t3po7re54]

For x sub 0 how'd you get 0 with 1/(1+0) ?

[GodSentJapan]

You just saved my calculus grade. Thank you for being awesome

[linkwigger]

Khan and Patrick should team up, imo.

[SonOfNye]

I just wanted to tell you that you cover a lot of material covered by the MIT lecture series and have a few thousand times their viewership. Go you.

[patrickJMT]

@SonOfNye yep, i have noticed that too : )

[Bludgeoned2DEATH2]

@SonOfNye Patrick should be teaching at MIT. Unless he already is.

[shootingrubber1]

Your videos are awesome. They help me immensely in my calculus class. Thanks!

[PANGAWD]

Man, in Portugal you take this during the 12th grade (last year of highschool). Possibly 1st year of college in Mathmatic Analysis I . On the second year you´re already cacting up with the Fourier series, Fourier integration or complex integration on Mathmatic Analysis III . But I really liked the explanation... simple and accurate. And I stumble upon this looking for the Simpson series from Fox! :P Thx

[J0searreaza]

You saved my life. Thanks a lot. Greetings from VENEZUELA!

[Kostas1601]

how can I prove that you can calculate the exact integral of any third order(or lower) polynomial with the Simpson's rule???

[LittlePokeDigi]

Could you help me regarding this question that needs to be solved using Simpsons Rule when f(x) is not given ? The Question did give a Free-form pool design but how do I find f(x)

[patrickJMT]

@twinblade00 n must be even for simpsons rule

[nutella871]

My teacher made this seem so intimidating. But you're right, it's a lot of tedious arithmetic.

Thank you for everything :) I've lived off your videos for the past 5 months, and will continue to do so at least for another week until my final exam! Then there's Calc II next semester...joy unbound.

Thanks again!!

[finalmaestre2]

Bro, i wish u were my calc 2 teacher.

[samiunderscore]

dude.. awesome video. thanks so much =D

[bokxybabee]

what happens if you divide the whole thing by zero?

[patrickJMT]

@bokxybabee the universe explodes

[p3rf3c7]

@bokxybabee then the answer would be 4

[mufiman1]

i love you man for this.

[peiznkev000]

haha! this is awesome. I'm using this (along with three other techniques) to estimate PI in a C program. :P

[charlesc300]

i got something different 1.44806 i guess cause the decimals i hope so

[noturno99]

very good!

congratulations!

[Feanic]

Hello patrickJMT,

Thanks alot for your educational videos. This really helps some people alot!

Keep on going :-)

[maxandwatson]

cheers pal. great help on a stressful day. lefties are always smartest

[LBDoctorJesus]

this might seem like a stupid question, but what is an antiderivative? its just im trying to teach myself maths :)

[RickRubik]

I know this is a little off topic, but what integration technique would one use to evaluate this integral?

[patrickJMT]

@RickRubik you would use partial fractions on this one.

however, not every function can be integrated using elementary antiderivatives, which is one reason why we need approximation techniques like this.

[RickRubik]

@patrickJMT That's a good answer. Thank you.

[imnoobshit]

@logeyDot93 but G is your mom...

[imnoobshit]

Thank you very much! I just had one on the test this week. {Question 6) Approximate ln(3) = intergate from 1 to 3 (1/x ) dx Using Simpson's Rule. Use n = 4. A) 1.098 B) 1.099 C)1.100 D) 1.101 E) 1.102 F) 1.103

[letterbombforyou]

In some books the formula they gave me was for "Delta x" was (B - A)/3(n) was that a typo from the book?

[letterbombforyou]

Oh I was wrong, I get it now (delta X) * (1/3) is the same as (delta X) / 3

[thatguywitcalculator]

@letterbombforyou no, it's because the formula is [(b - a) / n] / 3 which equals (b - a) / 3n. Remember your basic knowledge in dividing fractions. (b - a) / n divided by 3 is same as saying (b - a) / n times 1 / 3.

[benbrooks91]

Patrick, I love you.

[ITSxUNKNOWNx]

I honestly love your video it really does help a lot thank you so much

[patrickJMT]

@ITSxUNKNOWNx you are very welcome!

[SolidSnyder]

I don't see why Simpson's rule would ever be necessary...couldn't you just emply "u-substitution" in the denominator of the original function; [ u^-1 = (1+x^5)^-1 ]? Or does that not work when terms are raised to the negative first power?

[LukeTheShizzle]

I remember it like this:

h/3[ first + last + 4(odds) + 2(evens) ]

Easier to remember I reckon!

[WhaTango]

Very Helpful! Thank you.

[missjannine]

You are awesome, thanks so much for doing this for people who need extra help!!!

[irlzy]

is this is most accurate/useful way of approximating an integral?

[AgariRG]

How much do you make off the $0.99 Downloads? Is it quite a bit?

[jazzangelreloaded]

Oh one more question: you say that 1/1+x^5 is f(x); do you mean f(x) or f '(x)? I assume if we have the derivitive (f '(x)) and then convert it to f(x) we could use Simpson's Rule by slotting it into the equation.

[TrueShadowJS]

you explained the pattern 1,4,2,4,2,1 very well. thanks! my textbook did horrible

[AgariRG]

Hey Patrick. I'm learning this in high school right now and am curious as to what this is used for in life. Engineering? Astrophysics??? Accounting?! Lol. I'm learning this but I really want to know what this is used for

[patrickJMT]

@AgariRG well, antiderivatives have tons and tons of applications. not all functions have antiderivatives so some method of approximating them are needed; this is one of those techniques

[valberm]

@AgariRG basically, it's a building block for other applications.

[jazzangelreloaded]

you say that delta x is divided by n (in the 2nd line n = 3), but in the first line you say that n has to be even? Are the n and the 3 the same number?

[irlzy]

@jazzangelreloaded No, the 3 is a constant in the equation for simpsons rule

[ufofound90]

thank you!!!!

[4thKyuubi]

Is this also the midpoint rule?

[elten400]

super

[shimo1989]

Who the crap would do numerical methods in a CALCULUS course? That's just insane.

[happysleepyangel]

thanks for the great vid! I got the same ans as you ;)

[andrewnagi]

Hey, do you think if you have a bored moment with nothing else to do you could make a vid on using simpson's rule to calculate the volume of a solid revolution when rotated about the x-axis? Only if you're very bored!

Thankyou for this one!

[continentalvictory]

Thank you-great video. I calculated a rounded-off answer of 1.2416, but perhaps I should try again.

[kayrichards27]

Thanks so much. I'm doing independent calculus and I was so lost, but this really helped. Keep it up!

[trm6]

Wow this was so helpful! :D I was staring at a problem like this for almost an hour and I couldn't figure it out, but you've helped so much :D Thanks! :D

[paulio2293]

i like these videos. i did a degree in math some time ago, good to refresh memory from all that 1st year crap

[nishantnalinbhatt]

thanks ..i m getting 1.3276

[fofocuty]

thank you!

[annisdacoolest]

a south paw and no smug smarks......solid work there champ

[amjPeace]

The answer represents the area under the graph of the function, right Patrick?

[troubadorra]

Yes, integration is almost always findin area underneath a curve. This one is an approximation.

[buena0123]

if n= 2, wt will the equation look like? would this happen?

THX~

[karlkarlkarl1234]

Got 1.075 rounded off =) Tedious though.

[mackat4ck]

My textbook keeps telling me to do it with 5 ordinates! I'm confused.

[robbee1971]

Even number of divisions, which create an odd number (i.e. even plus one) of f(x) values to insert into formula.

[troubadorra]

Simpsons rule can only be use with n = some even number, are you sure that's what your teacher wants?

[dannyboy12357]

try integrating this lol its so complex. Thanks to S's rule this becomes quite easy

[kurtportelli]

thanks! you made me remember what my tutor taught me :D what you can do is to take 4 common for the odd numbers, and 2 common for the even numbers :) it really saves time!

[Wushu360]

I could learn calculus without going to school just by watching your videos!

awesome work man and thanks :)

[lkfh]

In your dreams sucker!

There's a sucker born everyday!

[jitterbug52]

omg ur amazing haha i have a test tomorrow and this was the 1 thing i was sooooo confused about!!! it makes sense now thanks!

[jumungjo]

thank u soo much again

i first did not understand Simpson's rule, and after watching this vdo, im ready for more Simpson's rule in my maths exam tomorrow

thank you Patrick :)