📚 Learn How to Approximate a Definite Integral Using Series - Step-by-Step Tutorial 📚

[@FaresTabet]

Thank you for existing

[@kevinmak1781]

Hope your graduation from college was smooth, 4 years later I also want to thank this man for existing

[@FaresTabet]

@@kevinmak1781 4 years later, i want to wish you a smooth graduation from college. cheers

[@abhaydhiman8192]

Wholesome 100

[@snipershot210]

This channel is amazing, you helped me so much! I'm a chemistry student and the complexity/difficulty of mathematics increased significantly from high school to first year of Uni. You are doing God's work! :)

[@Erolcem09]

SAME HERE!!!

[@tomatrix7525]

ZombieSlayer how does this relate to chem tho??

[@JiMMy-xd8nu]

@@tomatrix7525 It barely does, you're still expected to know this though. I guess the fourrier series have been used for stuff other than music, mainly physics I think. Look it up I don't remember exactly. Though idk about taylor-maclauren series. Just a useful trick to evaluate really hard calc 2 level integrals, or limits. I'm guessing they need to pass this course to get a degree of some kind in chemistry.

[@sibsbubbles]

isn't it crazy, and awesome that this educator's videos are getting over half a million views? way to go man. great teacher and simple explanations. saved me many times over.

[@abhinavkomaravelli65]

Hey Patrick, I've been using your videos whenever I have a little problem and you seem to have the solution with you multitude of them! I just wanted to thank you a lot!

[@zjguyer]

Likely taking my last math final ever today. This may be the last PatrickJMT video I ever watch to help me study. Just wanted to say thanks for your help these past few years! You're the best!

[@TheCobaltfist]

This is definitely saving my grade. My professor is a graduate student who can barely do some of the questions he gives us on the tests, but i learned more by watching a few of these 10 minute videos than i ever did in hours of class.

[@anthonywang7888]

Been helpful for years Patrick. God bless you.

[@squeezinthejuice]

I love all of your videos ! I'm doing Calc 2 independent study right now and i'm an audio visual learner hahah , ergo i wouldn't survive without these videos . Much thanks!

[@calibree2001]

It's 2018 and this video is still saving lives. Thank you!!

[@areebarizwan1977]

In 2020 too😂

[@emmanuellericher6945]

thank you so much for all of these videos! at the eve of an important exam, i felt really insecure about all these notions but they are more clear in my mind now!

[@engrxtianbautista]

The best math tutor in youtube :D

[@ReemAli505]

0:38 shouldn't it be (-1)^n+1????

[@nCzFx11]

thank you so much for being a brilliant human being

[@MrGittle]

You are a god

[@patrickjmt]

Jason K that's not what my wife thinks.

[@gnouveli]

atleast you got wife.

[@MrGittle]

Well that took a depressing turn

[@ana3zaz3liyaagadir7]

b

[@ana3zaz3liyaagadir7]

Michael G ,

[@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....

[@akhilkesavarupu7559]

Still think applying byparts would be faster to solve this particular problem

[@kevinhermosa]

Thank you very much dude! Your videos really helped me all throughout my calculus class :D

[@shrimatkapoor2200]

Don't you have to include the last term if it has (n+1) zeroes so that there aren't any rounding errors? In your case you are lucky because the 4th d.p is also 0 but if it was just 3 I think you would have to include it?

[@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!

[@patrickjmt]

i think i have one getting the taylor series for sin(x). you would do the same procedure to get cosx.

[@youngchang597]

Nice! Do you have a lecture on The Residue Theorem and Integral in complex number?

[@skulu]

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

[@SandboChang]

Thank Patrick for this great video.........I had tried to look up the Wikipedia in order to figure out what Taylor series guys are doing but it seems I wasn't intelligent enough to know a bit from there...........your video allows a really quick understanding of the application and importance of Taylor series, much appreciated.

[@mihirshroff1613]

Literally helped so much. Jesus. Thank you, my dude.

[@MultiXotas]

When you actually 'do' the integral, 6n+2 is added to the denominator. Adding 1 to the exponent was because he had an extra 'x' before the 'cos(x)' in the original function.

[@daniillitvinenko4348]

thank you so much! the last thing I needed to know for my calc 2 tutoring exam

[@SlapAndPop91]

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

[@gulsen1022]

Thank you so much for these videos Patrcik you are great!

[@gahtzuah]

You are a LIFESAVER. Thanks a ton!

[@MrNecro99]

Thank you, these tutorials are a great help.

[@AndySaenz]

This was very helpful! Thanks!

[@Valhala112]

They are so mentally blown away by @patrickJMT 's splendour and glory that they pressed the dislike button instead of the like button.

[@guitarhamster102]

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

[@nihaomz]

It felt good. Hey, thanks prof. Patrick!

[@yeeunchae4921]

Does the alternating series estimation theorem only apply to alternating series or could this method be used for any taylor series?

[@patrickjmt]

+Ye Eun chae alternating!

[@patrickjmt]

+Ye Eun chae there are other estimation methods that are more general though

[@seddie777]

Are you some kind of wizard?... You sir are amazing

[@patrickjmt]

we will miss you! :)

[@calculusmaster1]

you are truly a life saver. Thanks a million!

[@thuanvuinh4833]

Just need a pen and some papers. You have made great videos for everyone. Thanks a lot.

[@patrickjmt]

it is titled ' Taylor / Maclaurin Series for Sin (x) ' if you are interested

[@mrcooleh]

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

[@annydu34]

Why are the limits of the integral from 0 to 1?

[@billwindsor4224]

+Anny Du - those are just the limits of integration that Patrick chose for this example problem. (They don't have any general meaning other than that.)

[@JamesOfKS]

My guess is it's also more convenient for the trig since it probably cycles between some value of y over 0 to 1 x then repeats.

[@J7Handle]

Also Taylor Polynomials are really bad over large limits of integration. That's because the bigger x gets, the larger the error gets. Very quickly, in fact. At some point it sometimes becomes easier to use split the integral into pieces and evaluate a Taylor polynomial for each section individually (this is easiest when Taylor polynomials at different points of the function are simple functions times each other. You only evaluate one of them and the rest are easy. Ex: Taylor polynomial integral of e^x from 0 to 100 could be done by evaluating the integral e^x from 0 to 1 and multiplying by e for each next section of integral.).

[@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!!

[@patrickjmt]

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

[@23youwatch]

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

[@XJocoolX]

great video with lots of great information, but you may want to try keeping the paper in the middle of the screen in further videos.

[@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!

[@zmxncbvkkllp]

You just saved my Calc grade! Thank you

[@AllThatJazzLeo]

thx a lot b it is much better than other demonstration

[@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?

[@BigGus87]

This kind of problem i can do because our teacher had us memorize e^x, 1/1-x, sinx, and cos x. The problem is if you have a problem like 1/(1+x^4)^1/2 Can you manipulate the series from 1/1-x? Can you make a video on that? the problem is the square root. What can I do? I tried using binomial series for it and it didnt work.

[@dmelnick00]

what were you being asked to do. most of the time it helps to know what you are being asked. (I know its been 3 months, but for next time)

[@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

[@reeseweingaertner3735]

What would you do to determine the error if the series is not alternating? Thanks so much for the clear video though!

[@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!

[@deaksneaks]

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?

[@lutherm2011]

awesome video....you make calculus understandable....wouldn't have made it successfully without your help....

[@loik345]

Thanks Patrick for ur help.

[@RebeliousMoose]

Thank you very much. Helpful example and clear explinations.

[@erwin0504]

That's called an integration of x to the n-th power. If you integrate x^n you will get (1/n+1) * x^(n+1)

[@Jaggedrockz]

I am so confused as to why 1 was added to the exponent and 6n+2 was added to the denominator... what is that called?

[@MrWilsonlow1202]

may u explain this question for me?? y=sin^-1 (x), show that (1-x^2）y''=xy'....find the Maclaurin series expansion of sin^-1(x) up to x^5..thanks a lot :)

[@jennymurar]

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

[@JamesOfKS]

Patrick, love your work but tiny piece of feedback for me in my current class. I wish you hadn't put power series and alternating series estimation theorem in here... it's made this video force a learning of 3 things instead of just the Taylor series definite integral piece and confused the heck out of me. Would love a 'clean' video of just calculating a definite integral using Taylor series.

[@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) ]

[@unknownlove19]

i was hoping you would make more vids on taylor serieis thanks ! :)

[@deanrivers]

hey, I always watch your videos and it has always made sense to me. The only thing that i cant seem to figure out is how to find the actual power series in sigma notation. For example you said you knew that the power series for cos(x) was so and so. (in the vid). I just want to know if theres a video that you have that actually teaches how to get that power series. Thank you.

[@amanje407]

Thank you! Great video and explanation!

[@XTheDarthNiteX]

How would one use Maclaurin Series to approximate e^(-0.1) to for digits of accuracy?

[@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

[@thndesmondsaid]

Thanks for the video. Is there a way to estimate the error without dividing the numbers? I can't use a calculator on the exam

[@DoggoWillink]

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

[@paul7194]

It was so helpful, thanks a lot !

[@roseblack1301]

I am trying to approximate the integral of (sinx)/x from 0 to 0.13 and am coming up empty. I approximated the function itself, but can't seem to get the integral right. Nevermind, lol I was forgetting to integrate the series. Thank you for the video.

[@donkilluminati9484]

wait didnt he use a normal power series, not taylor/maclaurin?

[@rachelwalkowski5972]

I think the series he used was equivalent to whatever taylor/maclaurin series would have been used anyway

[@chrismarkwardt4685]

Taylor/Maclaurin series are variants of power series which follow the form used here to represent cos(x). Maybe you're thinking of Taylor/Maclaurin polynomials?

[@vyomapandya7908]

good job sir thank u so much for this wonderful vedio. we did not have to take a class for calculus

[@utahk157]

When integrating, is it always correct that we add 1 to the exponent and then divide it by that exponent? Pls see my comment since my exam is coming up and this video is my savior. It's just that I don't know if the integrating part is applicable for every case. Thank you

[@violintegral]

That rule only works for n≠-1. If n=-1, then the antiderivative of x^-1 is ln|x|+C

[@themanhimself436]

When you plug 0 in when doing the integral (Fundamanetla theorem of calcululus), and u get 0^(6n+2), doesn't it ultimatley become 0 to the infinity (after applyng limit). So it's indeterminate?

[@billwindsor4224]

+Clemmy Clue - we are tracking both x and n . So the Integral is performed over x (because the Integral shows dx ), so we evaluate the result of the integral from x = 0 to x = 1. So the bounds (from 0 to 1) are inserted for the x , not the n . We keep the 'n' separate for those steps.

[@themanhimself436]

I'm already almost done with my next calc course lol, but thanks for the reply

[@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.

[@ladhaya162]

I have a doubt ( using the maclarium series expansion for e power x approximation e1 correct upto 5 decimal places) upload the answer plz

[@joannelee5574]

THANK YOU KING

[@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.

[@and1fer]

God bless you.

[@sergefuni2141]

You're a bio chemist, you'll need calc to at least estimate the proper decay of certain isotopes in compounds, and several other things. Now I am a musician...what the balls am I learning this for!!

[@evanurena8868]

While I know this is six years ago but believe it or not, calculus is actually important in music as well because fourier series are used to calculate the pitch and harmonics of musical notes. Fourier series in it's basic form are an infinite series of sine and cosine functions with definite integrals as orthogonal constants of integration. So even musicians can learn calculus.

[@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.

[@MikaLovesKero]

@anny du the limits are given in the problem i think he forgot to put it in the video

[@150buckfifty150]

do you do physics too?

[@thepinkbed]

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

[@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.

[@engineer1820]

Its amazing! Thanks a lot!

[@mzwk369]

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

[@michelle1829]

so is this only for cosx ?

[@janblake5170]

you can use it with sinx too which is an alternating series you just change the 2n to 2n+1

[@J7Handle]

This is for any function you have a Taylor Polynomial for. Which can be a lot of functions. x^x comes to mind because the integral of that function is not an elementary function.

[@dangamage]

You are the best

[@tinkiniminki7712]

thanks for your existence

[@sergiolucas38]

Great video :)

[@Mardil]

you are my hero

[@Waranle]

Thank you Patrick :)

[@cynicalveil]

is that an iron ring?

[@themanhimself436]

That moment when you actually find a fucking vid

[@elitsa1992]

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

[@Benimadimyemek]

Allah senden razı olsun.