The Trapezoid Rule for Approximating Integrals

[MrToriasdax]

Also, It's nice how i can pause and rewind the video when I don't get it! Vs Math class, where everything's happening so quickly!

[MrToriasdax]

You make much more sense than my calculus Textbook.

I watched the video were you explained definite integrals, and now I just watched this one.

I Can finish my assignments now! Thank you!

PS- I've been sharing your videos with my classmates. :D

[EhtYlno]

thanks a lot Patrick! You're the coolest nerd I have ever come across!!

[patrickJMT]

@EhtYlno happy to help you

[EhtYlno]

seriously though, u're the best!! your videos have helped me countless of times... many thanks:)

[johnerhrd]

God bless you Sir Patrick for clarifying the Trapezoidal Rule for me!

[69lolwut69]

This was extremely helpful. Why can't my book be written in your words instead of making it so complicated? For some reason it feels the need to make every example with pi instead of just using a simple example like the one in the video...

[MrSnailshit]

am so glad you got a white board XD

[patrickJMT]

@MrSnailshit that was a long time ago. i dont use it any more

[TheOverdriver1]

how do u write dx/x to limits 5-1?? im just lost with the wierd fraction with dx LOL and our teacher wasnt a good help either LOL

[Thfro920]

Can you make a video about Trap Rule, but with unequal intervals?

[patrickJMT]

@Thfro920 you dont do it with unequal intervals.

[Thfro920]

@patrickJMT I figured it out but what I meant was essentially the proof of it that leads to the simple formula. It's basically taking the area of each individual trapezoid. The proof then distributes it to bring it to the normal trap rule. I asked my question poorly.

[vwturbo02]

Your video is awesome! Obviously you did a simple example considering you only used n=4. We are learning to use the sigma notation because we are dealing with n=50 but we are also using the calc and as a JMT fan you hardly EVER use calculators which may explain why you didnt do one like that. However I was hoping to find a more difficult one. Class ex was Intergral from 0 to pie/3 of cos^2(x)

[Tilade0]

Good video--however, my book uses Xsub(i) = a + i * Delta(x) for all parts N. Is one more "correct" than the other?

[1337Bigman]

In my book it says that first part is (b-a)/(2n). You wrote (b-a)/(n). Which is correct? Or is there something I'm missing?

[patrickJMT]

@1337Bigman there is something you are missing.

[1337Bigman]

@patrickJMT What am I missing?

[aargnok]

@1337Bigman In this video, he says that the constant out in front of the whole bracket is ((b-a)/n)/2 which is equal to (b-a)/(2n) :)

[Lukes808]

@1337Bigman he wrote delta x over 2, where delta x = (b-a)/2 and when you put delta x over 2 you get (b-a)/2n

[LizardanNet]

@1337Bigman Watch the video again dude, you'll get it...

[mirzconsulting]

Dear Mr. Patrick JMT, once again thanks for all your great videos, its not that my professor is bad, it just really helps to pause and rewind listen to something I don't understand twice. Your lessons are also to the point on the topic so I know to absorb all that is said which makes your lectures very efficient.

[bharathsf]

Hi, DO you have a video for Cauchy's theorem

[DjDonna5]

i wish you were my professor :) Thank you!!! you are awesome!

[Billabong024]

you are a god gift's to math students.

[patrickJMT]

@Billabong024 ha, just doin' what i can for you sweet, sweet people out there

[VeryOxygen]

Quick question, I need to find the approximate area between an integral function and a linear function (The curve of a parabola and a diagonal line dividing it into two). Someone help me understand how to do that?

[marsnarsx]

thank you so much!!!

[MaddeOC]

Thank you so much for this video! I was doing my assignment and I had no idea what the Trapezoid Rule was! This video did a better job at teaching me than my actual teacher has.

THANK-YOU!!

[TheLiz217217]

Thank you so much! Your videos are the best around, by far. They are great appreciated!

[jstrong151]

what if f(x) = 2e^3 + x^5 -3x . do i just find the numercial value for 2e^3 when approximating

[archuletarox321]

LOL @ 3:16... you smudged the left side of the picture because youre left-handed :D

[rykerh228]

I like the paper method instead of the marker board... so we can see where you've been

[wasabisquishy]

Thanks so much you taught better than my book and professor combined :)

[vekien]

THANK YOU!!

[gunmasta9792]

To make the formula easier to memorize/understand you could change modify it so that it is (f(x0) + f(xn) + 2(f(x1)+f(x2).....f(n-1)) or even easier (first + last +2(the rest)), please note that this is only for the part of the formula that is inside the brackets, the deltax/2 still needs to be added infront (I just cbfed typing it)

[ellethana23]

Can I just say how helpful this is? I missed the day we learned this in class, and I really need to know it for the AP test. Thank you so much for doing this for us!

[edijemeni]

Do u have any video on error analysis for trapezium rule?

[Starrynezz]

I was curious to know if there is a simpler way to crunch the numbers on a calculator or excel. I have both a ti 89 and a ti 84 and some of the problems I am doing are quite intricate. For example the problem I am working on at the moment is f(x)= (1+x^2)^(1/4) which is quite a bit of numbers to crunch if doing an equation with 10 subintervals.

[farlcoon]

@Starrynezz Just be liberal with brackets.

[sh4hb4zkh4n]

ahh yeah ready for my exam tomorrow

thank you sir :)

[valdivia562]

wow a million thanks i didnt know what to do in this section because our teacher didnt explain it at all, im glad i saw this video now i get it all.

[zucchini2007]

This example is much too simple...for my PDE's homework that I'm doing right now, I have a function composed of sin/cos fractions, multiplied by a decaying exponential function. It was the result of taking the inverse Fourier transform of u(x,t). As if that wasn't complicated enough, I have an infinite integral(an integral that goes from minus to plus infinity). How do I solve my problem?? Help??

[JLarry09]

i just needed to review because i ddi this a while ago. This was an excellent way to refresh my memory. The video and example was very clear and explained well. You might want to do some more complicated examples for those that are still trying to learn it though.

[gmkiely]

integral is X plus 1/3 X cubed. Substituting limits gives 45 1/3 which is very close to 46 given by Trapezoid.

[gmkiely]

Your videos are a great help! Might be an idea to integrate 1 plus X squared. Put in your limits and show Trapezoid approx is very close to actual integral of f(x) using the limits?

[SuperArglebargle]

I'm really disappointed, I thought you would derive the trapezoidal rule, not just mindlessly crank through it without any understanding of where it came from.

[patrickJMT]

@SuperArglebargle read your book. they derive it there. sorry to disappoint you m'lord.

[opoohsgurlo]

@patrickJMT Haha i laughed at m'lord

[patrickJMT]

@SuperArglebargle btw, this is so easy to derive if you were not so mindless and thought about it for like .1 seconds. i guess you need to be spoon fed all things. i used to have a teacher and he would tell students they were like little babies. now i know what he meant!

[NxGnBeastMode]

@patrickJMT LOL are teacher told us that too :P

[NxGnBeastMode]

@NxGnBeastMode our*

[shawondemand]

does n have to be even for trapezoid rule

[Sexygaston2000]

wait so you don't have to find the integral before plugging in 1,2,3,4,5? YOu can just plug them in strait?

[amirsabb]

i have another equation for this where the first and last integral is divided by two and the inner functions stay the same, is that the same thing???

[yisoonshin12]

What I really like about your videos or really any type of learning not in a classroom, is that the teacher doesn't have to constantly stop and say some variant of shut up. But even better about your videos are that you're serious and confident, but have a joking manner. i don't know if that makes sense, but whatever.

[amberfrost28]

you are amazing. sooo helpful. THANK YOU.

[123MrDinky]

thank you patrick. but in other formulas they have been using: delta x/ 2 *n.

[MsShamma123]

what if n is not given in the question, how do we get it? could u give an example please?

[danizacash94]

what if delta x is 2

[dragonfire84724]

@danizacash94 the you multiply everything in square brackets by one since 2/2=1

[askjeeves28]

the only thing i didnt understand was the value of z, when he did x/z. why was it 2?

[RogeerBoy]

I just your videos to review before a test so thank you man. My new way of studying.

[slyker25]

Cheers from New Zealand

[michaelschnikel]

You are my hero! Thank you sooo much for posting this!

[EViEMAE]

Thank you so much! I was absent for this lesson and I understand it completely in only 7 minutes! Very clear and concise. I am definitely going to watch your videos further to get ahead of my classmates hehehe ;) I love math <3

[J0searreaza]

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

[ipavdekshmi]

Thnx a lot...cheers From Albania

[kleinrider42]

Do you love what you do Patrick? Does tutoring pay well? This is so interesting.

[j1015379]

every calc exam I come straight here, I've been streaming for 12 hours straight now cramming 3 chapters, if only her tests were strictly problem based =[ she is crazy on the concept stuff, but thanks man nice work

[andwhynotgrant]

oh man this is awesome, i have a test on this tomorrow and an indecipherable teacher. i think you've saved my calculus grade

[Digadogup]

nice vids but could you please link our videos it'll take 20 mins for you but save many hours for your viewers .

learn more here then in school

[flyhalfinoz]

thank you very much patrick!! u've made is soo easy to understand!

[9096934137]

I'm confused as to how the trapezoidal rule gives an average of the right-hand and left-hand estimates done with rectangles.

[chaoskie]

why does my text book note the formula having ( b - a ) / 2n while your video shows it as only ( b - a ) / 2?

[arsevela33]

@chaoskie the formula is actually DeltaX = (b - a) / n

n being the number of strips or rectangles u use

[WHATUG]

This is cool. Thanks for the post.

[livinglinkz]

Oh my freaking god! my teacher at school giving us problems like this without even explaining to us how to F****** do it or where and why it originated from. Im beginning to hate her even if she is a harvard graduate.

[omgitswes32]

say that a is 1 and b is 2....how do you go about finding the midpoints then?

[anhvnsvns]

he's great ! using left hand for write these thing

[luisyahh]

Holy sh**, I hate Integral Calculus. :S

[mpatt79]

what am I missing?? I've seen it this way..... delta X = (b -a)/ 2n........I think what you're using is just (b-a)/ n ........... are you taking the 2 into consideration? Shouldn't a 2 be in your calculations in getting delta x ??

[JDMimportsFTW]

You should become a tutor. Neat writing, easy to understand, clear voice, know what your doing and confident in your work. Can make a lot of money on the side if you do tutoring. Thanks for this video.

[patrickJMT]

@JDMimportsFTW i make a lot of money doing it full time, but thanks for the recommendation : )

[patrickJMT]

@JDMimportsFTW it is part of the reason i do not teach any more (but only part)

[michalchik]

@patrickJMT Ditto

[Digadogup]

@patrickJMT your too good for tutoring lol

[ilhamchi]

thank u patrick for the video :))

[tronulu]

dude!

wrong hand!

[nikhil5556]

Thank you Patrick! this helped me so so much, you see my teacher is pretty shit and this is helped a lot.

[simrenism]

what if u have a number before the sigma sign and u have values for ur 'b' and 'a' and u have to apply trapezium rule and simpsons rule

[motomodder123456789]

thanks for the video Patrick! I have an exam on tuesday and this has really helped me :)

[patrickJMT]

@motomodder123456789 great! once you do a few and understand the notation, these problems are not too bad, just uber tedious if you have to do it by hand.

[dgamma1]

@patrickJMT you could use the rule: 1/2w[E+2M]

[seven0ate0nine]

thanks so much dude! Calc AB exam in the A.M. You are a lifesaver

[konradLxS]

safe

[mzmidnite]

I know you've probably heard it/read it thousands of times, but honestly, you are my HERO. Thank you so much for all the videos. I've watched just about all of them that pertain to Calc AB and I have my exam in a few days. Thank you so so so so much! Thanks to you, I'll be saving a LOT of money in college because I won't have to take calculus again (hopefully!) :)

[patrickJMT]

@mzmidnite good luck on the exam!!

[zelda127]

i  love you

[DrearierSpider]

the first time my professor taught me this i walked out of the room less intelligent. these videos are the only reliable way i have of learning calculus

[romanserp]

man go teach math at some high school...you will have some great minds

[splint3048]

My book shows a method which looks simpler.

Delta x( (f(x0)+f(xn))/2) + f(x1)...f(xn-1))

I just saves multiplying a lot of stuff.

[xwewx]

LEFT HANDERS FOR THE WIN!

[XxDecrepifyxX]

wow watching this video one year to the day it was created :]

[majorpun]

duuuuuude! math-nerds review!

[ScoobySnack102]

How do you figure these questions out if you're NOT given the "n" interval????

heeelp!!

[Rohan233]

the 'n' interval is ALSO KNOWN AS: An Application, Strips , or Sub-Intervals

[troubadorra]

If they don't give you the 'n', they will give you the error margin. From that you can use |E sub T| equals OR IS LESS THAN [M (b-a)^3]/12n^2

And solve for n.

[tanner6159]

forget that last post i see how u did it now by finding delta x. my bad.

[tanner6159]

ur formula in the beginning is wrong. the coefficient in front of the bracket should be (b-a) / 2n.

[DeiSanyu]

Here's a simple way to remember it everyone

h = (b - a)/n

A = h/2 ( First term + Last term ) + 2( the rest of the terms)

" = "(approximate)

[kennypillow]

Do you think that many students would like to know why the middle terms are doubled and the outside terms are not?

[scdlbrdr]

because your taking the average of the y values of each interval.

[x0)+x1]/2 + [x1+x2]/2 + [x2+x3]/2 + ... see how you how you have 1 of the end terms and 2 of each middle term?

[troubadorra]

It's fairly simple: The legs of the trapezoids not at the ends are used twice.

[bluemarron86]

sorry..im not really good in math...im just wondering, why do we have to approximate? cant we just solve it using the simpler methods taught in integral calculus?

like, the integral of the function you are using is x+(x^3)/3 , which when we evaluate given the upper and the lower limits is equal to 45.33

our teacher gave us an assignment to explain why do we have to use numerical integration?

please help me

[zestoney]

Sometimes an integration is either impossible or too hard to do any other way.

[davidenelson]

@bluemarron86 you use it for functions that cannot be integrated

[tree5821]

wow thank you!

[naomi1634]

All of your videos are sooooo helpful!!!

[isamedicin]

Thanks a lot its really helpful!

[kashiark]

so you half the first and last? why?

[aqualizard2991]

i am not religious but ...you are a god!

[122123456]

omg this was awesome!!! u just saved me from failing y maths exam!!

[ymichael90]

Thank You for all your fabulous videos.

Could you do simpsons rule and the error bounds please.

[manzoor1]

Patrick, can pllease do an example of

the Error bounds for Trap, Simp, and midpt. Thank you!

[pew2007]

Great tutorials.. very helpful

[cosm0]

Thanks! Excellent tutorials !

[gamemaster014]

wow it's good to know i have a math tutor like you at home

[TheDuskMar]

What happens if you actually integrate that?

[patrickJMT]

you get the exact answer

[TheDuskMar]

that, actually wasn't what I was looking for.

What is the exact answer in a number? :-)

[theLichKing1]

you get 45.33

[patrickJMT]

thanks!

[patrickJMT]

could not help being a bit of a smart ass. that is just how i roll....

i know, i was just too lazy to figure it out.

thelichking1 suggests it is 45.33, which i am going to agree with.

thanks LK1!

[roderik1990]

@patrickJMT that is correct, the exact answer is 45+1/3

[tenken1337]

omg 46/2 = 23. It's EVERYWHERE!!! =P

but seriously, thanks for the video. We were just about to learn this tomorrow and I really didn't understand what my book was saying. Keep up the good work! =)

[patrickJMT]

23, coming to get you!

[parvinhasan]

[to watch this video in Hight Quality: add &fmt=18 after the url of this video..]

I was waiting for this video..thanks for posting..

[patrickJMT]

no problem. not the hardest example, but i hope it helps!