Using Maclaurin/Taylor Series to Approximate a Definite Integral to a Desired Accuracy

[BER2ERKER]

The (-1)^n just comes along for the ride. I thought he was just going to be chillin' out there, but you never know.

[stephenpawn]

How are you doing this???? Who are you? A college professor?

[jennymurar]

How would you approximate if it says "degree 21"? i never understood what the degree stood for.......

[thepinkbed]

The Taylor Remainder video is private? :O Can I be your friend?

[melisantika]

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[Onepissite]

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[Ondelendo]

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[bebeheuy]

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[willamricard]

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[imegatrone]

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[anakmudajaman]

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[calculusmaster1]

you are truly a life saver. Thanks a million!

[genrytov]

I have a tough question, I was looking online for all the "base" power series representations (like the one you used for cos(x), but I could not find a whole list of them all. I know the one for e^x, sin(x), and cos(x), but where can I find the rest?

[elitsa1992]

@genrytov search for wolfram power series expansion calculator or something like that

[OMGITSLACKO]

Awesome video dude, thanks, If I ever pass, It will be because of you! :)

One thing puzzles me though: I can't figure out what to do if my taylor serie is just full of zeroes like with this one: (x^5)/(1-x^10) around 0. I just keep derivating but all I can make a sum out of is zeroes... What am I missing?

Cheers

[Rhakimdar]

Just wondering, why or how does 0!=1? Is there a proof of how it can be defined this way or did people just say it does so we can avoid a 0 being in the denominator? Thanks, love ur videos!!

[FireUni1]

@patrickJMT thanks for the vid. How can one find the power series representation of - 1/1+x^2?

[alarsen6857]

Ahhhhhhhhhhhhh... so confused

[ckim336155]

Love your videos, but I'm in constant awe at your neat handwriting. It's ironic, but it's so neat it is distracting!!!! lol j/k

[RaqibulHayder]

I hate Sergio Schanchez!!



[Carlos64073]

I GOT IT !!!!!!

[Onlythefinestwilldo]

@mutantninjafly Yes, please stop shaming chemistry.

[javilopez84]

I have a problem that i don't know how to calculate:

I have to stimate the error when i use the 2 order polynomial of Maclaurin to calculate the definite integral of x*exp(3x-1) from 0 to 0.2. How could i do it? THank you very much indeed

[rykerh228]

23 tutors lost their jobs and disliked this video

[FrOsTStrYke]

I'll never know why a lot of people dislike calculus and think that it's useless. It's one of the most fundamental things you have to know in scientific and engineering fields. It's almost like if I said algebra was useless in grade 8.

[pharmj101]

I dont think i could get through this calc class without these videos. BioChem major also and you have to know calc to understand chemistry otherwise your a trained monkey. Example basic chem integrated rate law... Thanks for the great videos!

[DrumAngel09]

Thanks for the tutorial, very useful. My only question: is there a quicker way to find the exact answer? Or is the best method evaluating the definite integral at each n?

[emoshoes11]

You. Are. So. Amazing. 

[guitarhamster102]

I'm a bio major who probably never use calculus again after this semester. Thanks patrick I love you.

[huan1217]

I dont need to go to class anymore, I can just sit in front of computer and watch your videos and pass the class..... screw thoes useless professor.

[dreamstyle22]

Its amazing! Thanks a lot!

[titan59]

@voidwareprohibited I dont understand why a chemist needs to engineering/solving problems in MATlab. And i fully understand the use of calculus in the sciences, like differentiation and integration and a couple other things, but series and sequences? I dont know. . .

[claridad007]

@patrickJMT : you are AH-MAY-ZING!!! :)

[wildbluefaerie]

thank you! you've done what my calculus book cannot and actually explained something so it made sense.... you're a life saver, seriously.

[Jaisz]

Good Stuff , you're very clear and concise, gotta say the add in the middle with the volume spike kinda sucks.... understand the adds but not sure why youtube has to spike the volume, most people watching are going to sit through the add to get to the end anyway ..you are a big help.. thanks

[dem0nthesis]

Bah, i wish youd do a simpler one lol, im not in engineering calc!

[150buckfifty150]

do you do physics too?

[MutantNinjaFly]

Why do I have to learn this? I will NEVER need to know calculus to be a biochemist, by my degree requires it. And if I do need to know calculus, then I'm already done in anyway because I ABHOR it and SUCK at it and would have to give up my passion to go find something I actually can do well. Guys please tell me I will pretty much never use this waste knowledge in my job.

PS thx Patrick, I may hate calc, but I need to keep my GPA up. cant do it without you!

[patrickJMT]

@MutantNinjaFly glad you like the videos but... do you complain about every class outside of chemistry, or just math? do you really think that math (calculus) has no place in chemistry? i just did a google search and found a ton of places where calculus is super important in chemistry. you remind me of a student i had once who wanted to be an engineer, but hated calculus and felt it had no point. i just gave her a blank stare when she said that....

[MutantNinjaFly]

@ell, I sort of know that yes, I need some calculus, I just lament it, and not because the material is super boring, but because it frustrates me. Yeah, I guess I am being rather winey, but then again I did write that at 4 AM when i was very tired and frustrated. Sorry to trash something you probably care a lot about, that was rude of me.

[dem0nthesis]

@patrickJMT Agreed, im a biochem major, you don't need chem for the undergrad stuff, but if you want to go to graduate school you need to know the problems inside and out, without calculus functions you can't do that.

[07ziul]

@patrickJMT

LOL

[liquidstl]

@patrickJMT Patrick, I'm studying engineering, and I would DEFINITELY be Lost without the 3 semesters of Calc. and Differential equations i've had... Just following along in a lecture or reading a text book Requires knowledge of at least the ideas in calculus, such as surface integrals, Laplace transforms, derivatives, gradient,etc... so just saying that I AGREE with you, and found this person's comment to be funny as well as a little ignorant.

[virginialikesyou]

@MutantNinjaFly My Chemistry teacher who has a PHD in Chemistry said calculus is the single most important thing to learn if you are serious about science. They use it all the freaken time! He suggested that I take all the Calculus offered because it is used on a regular basis for Chemists and Biologists. (I am a biology major too.) You just have to do it and you might as well learn to love it because you're gonna be doing calculus for the rest of your life!!! Change ur attitude.

[Bugga951]

@MutantNinjaFly Tip: You suck at it, because you abhor it. Pretend you like it. Sit forward when the instructor is talking. Say to yourself "I think Calculus is awesome!" Because 1/2 of truly feeling an emotion is expressing it. This probably won't apply to you now but it will help in any other subjects that you "abhor." and I know it sounds ridiculous but it works.

[kseslayer]

@MutantNinjaFly

ya i dont see how you think math has nothing to do with bio chemistry...

a) chemistry is the science of electron physics which is described by linear algebra and calculus (ie electron densities, quantum physics)

b) during experiments you will have to extrapolate values and with out calculus it would be impossible to determine the equations that describe the system your working with...

ring theory<linear algebra<calculus<physics<chem<­biochem<bio< everything else

[bvmassacre]

i watch your videos right before the class corresponding to the video topic and right before the tests..math has never been easier. Thank you PatrickJMT <3

[remirap]

u bent ur marker caps clip thing haha

[Mach5iv]

THANKS PAL....buddy. You made it seem quite standard.... and beautiful.

-Dirty mike and the boyz

[loik345]

Thanks Patrick for ur help.

[Blazinman12]

after watching almost all your videos i just realized that you are a lefty... weird... i dont think i can watch you anymore ...lol jk man you've been a ton of help, thanks!

[ramhamla]

wtf, why are ppl disliking this, so helpful

[patrickJMT]

@ramhamla well, ya can not please everyone all the time! especially on the internets...

[kx32ta1]

@patrickJMT (not complaining just trying to help) I have an idea why the dislike on this one. The way that it was taught in class is alot simpler than this way so it is probably confusing people. We were taught to fill in using maclauring chart then integrate. Once integrated, solve each term and drop the ones that are less than 5x10^x (x power = 1+ the desired decimal accuracy) Then the rest is history. Thanks.

[cyrus93]

@ramhamla haha i'm pretty sure the dislikes are about the content; there's no doubt the videos are super helpful but god damn i hate this part of calculus. i do see its importance though.

[demoshe2002]

You need to decline all those Michelle Bachman commercials! They are distracting because she is pretty and dumb..lol

[RebeliousMoose]

Thank you very much. Helpful example and clear explinations.

[mzwk369]

lol, i just figured out my teacher teaches us according to your video!!! you rock and he sucks!!

[SuperTari123]

@mzwk369 oi so lolworthy

[anar212]

thank you.

[TheRozworld]

So helpful most textbooks use such difficult examples that make no sense. When you look at them you just want to give up. Thanks a million

[23youwatch]

Hi Patrick,

i was wondering if u had any videos on the approximation using the taylor series and taylors inequality... ?

[MrNecro99]

Thank you, these tutorials are a great help.

[RuralJuror]

thanks :)

[mrcooleh]

thanks alot man, you make it seem so much simpler.

[infantileretard]

Great videos man. Can you do one explaining the Taylor's theorem in some detail? Like go through the proof and explain the processes with some fundamental logic.

[alexxxandre91]

im at my first year of electrical engineering  and we are doing this right now! its kind of hard.

[yonijar]

thank u for the video.

i wanted to ask if there is a way to find out to what value the expression you got, in the very end, convergence to?

[ it it an alternating series with value that goes down i.e. it is converging (leibnitz) ]

[deaksneaks101]

At what level is this? I know that America and the UK may have different systems, but i'm in year 11 (roughly 10th grade in America I believe) and have done my AS level a year early.. But am yet to do my full A2 level in year 12 at sixth form (non-compulsory Education).. I pretty much understand most of your stuff, such as exponential and logarithm functions (since they're in core 3/4 of A2 level), but this is the only vid (so far) that I don't get so wondered at what level this is, if you knew?

[Jmerino7]

@deaksneaks101 This is calculus I or II. Just remember what you learn in algebra, and precal and you should be alright. This would be 12th grade in the U.S. for less then 5% of the high school population in the u.s. maybe more or less. But some take in the university level.

[cacaloveforever]

we did that in class. cool

[SlapAndPop91]

Thank you so much! These kinds of problems have been botherig me all week.

[thegambitking]

I'm a bit confused, since on my homework I had cos(x) quantity cubed, and not cos(x quantity cubed), and i got the exact same series, even though they're different functions (and it says i was right in the back of the book!) ... do these just happen to equal each other, or did i make a mistake? Oh, and thanks so much for your videos... they're awesome!

[mrdevecseri]

how do you do this with the taylor inequality?? in other words for a non-alternating function like f(x)=e^(2x)

[mrdevecseri]

how do you do this with the Taylor Inequality??? in other words for a non-alternating function like e^(2x)

please help, i have an assignment due wednesday :P

[Yewtubex3]

Thank you soooo much!

[TSS888]

awesome. I have a calc test tomorrow and this video saved me. :)

[sammartinross]

FIrstly, thank you. Secondly, you mentioned you think we should know the power series for cosx, is there any others that we should know? and could you tell me them. Thanks again

[mysticalkittys]

thank you so much! this tutorial is so handy! i was actually doing my calc hw and i didn't understand the taylor series so i got bored and went on youtube to watch videos. haha who would've known that one of my subscription video was on the taylor series! haha. thanx again!

[mducky6]

Is this BC Calc?

[Waranle]

Thank you Patrick :)

[Mardil]

you are my hero

[UnFisicoMatematico]

your batman

[yardy12]

great job

[alcyonae]

you have the ability to post the right videos exactly when I need them :D thanks!

[unknownlove19]

i was hoping you would make more vids on taylor serieis

thanks ! :)