Calculating a Definite Integral Using Riemann Sums - Part 1

[halospartan5]

This guy probably got laid every night in college. He makes this shit look so easy

[patrickJMT]

@halospartan5 women dig guys that can do math

[ronniemonnie]

Why do we use the formula a + (delta x)i to calculate xi*?

[patrickJMT]

@ronniemonnie well, label points on the number line: x_0, x_1, x_2, etc and find a formula for their values.

[HaydnM35]

MARRY ME

[TheBright01Star]

thanks you made it so simple =D

[dala555]

this seems like an overly complicated way of doing something very simple.

[legoindianajones1000]

@kdizzle20901 yes

[legoindianajones1000]

Can reimann sums be used without a function, just points on a graph? Let's say I have 30 points on a graph, to calculate the area, will I have to do middle,right, and left endpoints to get it? Or can I use reimann sums?

[TearfulCar1]

so much better now!!!!! Thank X1000000000000

[Alandar2030]

great! thank you. I finally understood this crap! God bless.

[cwidman99]

asthma attack averted @ 4:46

[8644371]

I've learned sooooo much calculus from you.

Never took it in high school. And the college won't let me take it yet.

You. Are. Awesome.

[OhHiMeMatt]

Once you go pat, you don't go back

[Dewskiz]

This helped me out a lot.

...but I still hate Reimann Sums.

[KewalaKetcher]

thanks man great explanation

[Jezebel1115]

Thank you!:)

[sweetsaphire23]

omg thank you!!!!!! I CAN PASS MY CALC TEST WOOT!

[MrDkt92]

hey thank you this was very helpful. I was trying to find the definite integral of 1/x..using riemann's sum with left endpoints...but i'm having some trouble evaluating the summation...i'm getting something like the Sum of i=1 to n of (3/n)*[ n/ (n+ 3i -3)] idk how to evaluate this

[secyborg]

thx for the great info pat! i got one question tho...what should i do if they give me 6 for a value of "n" and a=0 and b=3. delta x would be 1/2. is it possible to evaluate without the delta x having an "n"? Also, how would you set it up if they give tell you to take the sample point to the left, right, and midpoint?

[FeelingFreshSon]

I've learned more about integrals today than...well, than ever, considering I didn't know much to begin with. thanks!

[jduval677]

Thank you sir.

You really didn't explain it any differently than my prof...but the fact that you seem to actually understand it and comprehend what you're doing makes a world of difference.

Hugely appreciate you taking the time to do all these.

[henryk8675309]

If I get an A on my test in 2 hours I owe you approx. 235 dollars

[lingolatz]

If you are wondering what x sub i^* is, you need to watch the preceding video, v=LkdodHMcBuc

[ColeOfCentauri]

What are the rules on combining and distributing Riemann sums? Would it be right to say that Sigma(a_x)/Sigma(b_x)=Sigma(a_­x/b_x) if the parameters on the sigmas are the same (say, like from x=1 to n)?

[BillieBaby143]

If an interval starts at something other than 1, doesn't i=1? Do you still put i=1 under the sigma?

[angelicasald10]

You just totally saved me.

[HoUsEoFlAsTwOrDs]

I want you to know this video helped me so much. Thank you. I was having a lot of trouble with the manipulation, but this cleared it up. You are a wizard and a scholar.

[tupacsomething69]

you sir have single handedly replaced my lecturers, and i go to university of sydney

[lolkiwi]

I'm glad to say, my calc 2 teacher is as good as Patrick..woohoo!

My calc 1 teacher was horrible though.. and I still like to check Patrick's videos, they're still very useful. :)

[JLPOSU10]

How do you calculate square root of x+5 with lower limit of -1 and upper limit of 1.....i am confused

[daniellalyssaa]

thank you @patrickJMT !! this video definitely helped me out. Im taking calc 2 at UTSA for a 5 week summer session and my teacher isn't allowing us to use calculators or anything so learning this the long way is exactly what i need, especially since our exams are all written.

[pacsgambati]

@patrickJMT do you think you could do an example of calculating the riemann integral using upper and lower riemann sums for a piecewise function?

[iamradsara]

thank you for posting this video- it really does help!

[VeronikaCity]

AP Calc tom!!! Who's ready! haha

[CehJota]

@VeronikaCity not me.

[obscene678]

Omg Based God

[1wowfactor]

My Calc. teacher is better than this guy

[FUSCheaters]

@1wowfactor haha so you watch this video whyyy?

[1wowfactor]

@FUSCheaters for the fun of criticizing. lol

[FUSCheaters]

@1wowfactor Sounds fun

[imvanessavella]

in the definition . is it always i=1 ? is there any instance that i= 0 or other number ?

[sh4hb4zkh4n]

why are all the good teachers only on youtube?

[Slappydappy]

What exactly does "x of i star" in this video represent? The way it's calculated is giving me the right interval point of the rectangle.

[patrickJMT]

@Slappydappy it represents any point in the ' i-th ' interval. the idea is that you really do not have to use left endpoints or right endpoints in the definition; all that is needed is to take a point from each interval. the x-i notation is pointing that out.

[Slappydappy]

@patrickJMT If your calculating an Integral don't you need to use midpoints? Or does it not matter?

[patrickJMT]

@Slappydappy if you are approximating an integral, you can use any point in the interval. to prove that an integral can be calculated by antiderivatives, it turns out you can again use any point in the interval.

[missioana8]

@patrickJMT you could use Leibniz-Newton formula. this one is too complicated.

[Arbitore]

Teacher gave me this stupid example of how to do this question and it was the worst made no sense at all, essentially you saved my life. Oh and btw LEFT HANDER REPRESENT!!!!!

[fremsley001]

You can also calculate definite integrals by drawing the function as a curve on a piece of grease-proof paper, filling the area underneath with a uniform layer of cream cheese, then carefully scraping it off and weighing it on kitchen scales, giving the answer in "Philadelphian equivalents." This is the way Riemann himself did it before he hit on the idea of his sums. (PS. Andrew Wyles used cough drops and teaspoons to prove Fermat's Last Theorem.)

[patrickJMT]

@fremsley001 that is f-in hilarious

[farrananderson]

@fremsley001 I just randomly busted out laughing in the middle of the library. Thanks :)

[qwertymouse2010]

you made learning 6 chapters of integration in one night possible! You are my hero!

[hubomba]

Is it RYEman sum or REEman sum? Anyways, thanks for the help. My teacher (AB class, still in high school) tends to get too involved in his explanation of things. You are really good at just getting to the meat of the concept. This is helping me preparing for my AP exam, keep it up.

[nurpandbutch]

SHOW YOURSELF!

[BrucasIsBettaThanYou]

YOU HAVE LITERALLY SAVED ME FROM FAILING.

Thank you (:

[MsZenshi]

VERY GOOD ;) DO YOU ALSO HAVE TUTORIAL FOR WALLIS FORMULA?

[pankajghildiyal]

Thank you so much for uploadin such great videos......... !!!!!! I am a 12th standard student from India nd I get a lotta help from u........... It would be greatly helpful if you upload the expansions of various functions like sin x, cos x, tan x, e^x, log x and why and how do we use them in evaluating the limits. like e^x = 1+x/1! + x^2/2! +.........so on....... sometimes we use them in limits right ??....

[martmelee]

man , i got this by just watching your video, and i couldn't get all that with one and a half hours of class , and my native language is spanish.. so you get the idea how crappy my teacher is :(

[Bleachnarutoawesome]

I use your videos to get an idea of topics before we cover them in class. According to this video, it seems that integration is much more interesting than differentiation.

[firzennet]

@Bleachnarutoawesome it is cause differentiation is functions to slopes, but integration is slopes to areas to volumes! and more

[jb4ll3rrr]

thanks man. you are my savior!

[HREL7]

Way better than my math teacher at explaining! Thanks

[patrickJMT]

@HREL7 very welcome!

[NMelakis1]

Thanks this really helped 

[RRadRussian]

That was extremely helpful. I knew all this stuff but wasn't able to glue it together.

[koukla008]

Why did this video stop working? It looks really helpful 

[GrifoMTL]

you guys should watch this when you dont know what this is about xD

[Silvertooth]

OH MY LORD YOU ARE AMAZING. Calc final in less than 12 hours and I almost gave up on trying to figure this out but THANK YOU.

[evan773]

Left handed! me too!

[Username93611]

That's an awful weird looking Sigma.

[jityr2]

Who the fuck keeps putting ads before the videos? It's annoying the shit out of of me.

[eryn922002]

He sounds very annoyed. A lot of help, but not Sal. Sorry bud.

[Zatono12]

Dear Riemann Sums, I hate you.

Dear patrickJMT, thanks for making this a little easier.

[hellomynameisla]

4:45 epic math breathing

[ballwizard6]

Thanks!!!! you saved my grade 

[bf2gamestotal]

aweasome job on youtube!

[dannyp2432]

Patrickjmt, your the best at explaining math thank you very much.

Zeno1999 a hero is respective to personal opinion so I don't see why your trying to be so technical about someones comment. He is praising the man so just let it be.

[gaaralover9416]

I love you so much right now haha. I have a test tomorrow in AP Calc about this and you helped me more than my teacher haha

[Rondoplease]

yo pat for (1+2i/n)^2 i think its 1+4i/n+4i^2/n^2 not 1+2i/n+4i^2/n^2

great vid!

[IIrenzoII]

to calculate Xi, u used a+∆x, and that is for the left endpoint, but what about the right endpoint or the middle one? what is the formula?

if u could answer me this question it would be greatly appreciated :)

thx in advance

[fandanstan]

First year calc = solved! Thanks so much!

[TheGerbilFactor]

Are you sure you aren't Issac Newton's illegitimate greatx10 grandson?

[SquirtleScott92]

So i was studying for my Calc 2 miidterm and i realized i had no idea how to do this because i slept through lecture one day. It is currently 1 18 Am and my test is in 8 hours. I now know this so well. You are my savior!

[Wassup148]

Goodness. You made this so simple. I bow to thee.

[daddygreenjeens]

patrickjmt I just discovered Second Life and it seems it is in severe lacking of education.....i bet you could tap in to that market a bit too! let me know if you already lecture on there.....i've attended a few actual edu courses in philos and music but none yet in mathematics - your videos have been a staple in my last 3 A's ive gotten in school i wanted to share this with you (even though I'm sure you're already well aware of SL) Thanks and keep the vids coming!

[Starpluslover]

sir i hope u were my prof my prof sucxzz like srsly =[ buh ur the best

[Saladon89]

F-ing brilliant. many thx dude.

[germany7799]

ROFL AT TRANSCRIBED AUDIO

[annoyingmish]

DUDE PLEASE TEACH AT MY UNIVERSITY..... The American University in Cairo!!!!..... THE TEACHERS FOR CALCULUS ARE PATHETIC!!! I love these videos btw.... I used them last semester for Calculus 1.... KEEP IT UP DUDE!!!!!

[nnoplacetohidee]

thank u soo much !

[GuyMcpersonLol]

you sound really annoyed everytime you sigh

[patrickJMT]

@GuyMcpersonLol well, maybe i was tired or sick or just pissed off when i made this video

[derobmai]

@patrickJMT i make the same sound when i do definite integrals. lol in fact i make the sound whnever i do my homwork D= HAHA!!

[MonaRocks09]

you and khanacademy are HEROES you deserve noble peace prizes!

[patrickJMT]

@MonaRocks09 ha, well, at least salman keeps appearing on the news ; )

[hasben0]

@patrickJMT

yeah,whats up with that, i think its your turn to be on cnn not sal.

[Prolocater]

@patrickJMT I think you deserve the same recognition because you go more in depth

[Palmar3s]

@patrickJMT

yeah. you should get an award or something too!!!!!

I'm totally nominating you for teacher of the year!

[Zeno1999]

@MonaRocks09 < Regurgitating math solutions doesn't make someone a HERO by definition. You may call these teachers, dedicated professionals and give them respect they deserve.

eg. Mr. Nelson Mandela is a hero. Riemann the great mathematician and researcher could be called a hero too. So are many soldiers/police officer/firefighters.

[MonaRocks09]

@Zeno1999 um no, dedicating time to help others and expecting nothing in return makes you a hero. so just stfu, crawl back in your hole and die

[patrickJMT]

@MonaRocks09 hey mona, some people just are pissy people and like to argue and criticize others. do not let some d-bag on the internets piss you off ; ) some just having nothing better to do in life than to try and feel important and pass their misery on to others.

[Rogli]

My very quotable teacher in Fourier analysis said that it's a disgrace to associate a big mathematician like Riemann with the depraved definition of integration that is the Riemann integral.

[86PapuCho86]

How about double integrals? How do I do?

[Eneas724]

That integral is pretty easy, there is no need to use that method lol

[patrickJMT]

@Eneas724 lol, thanks.

[emeraldskull]

OMG THANK YOU SOOOO MUCH!!!!! it legit saved my life :)

[MultiRayKing]

1:56 "and so we went actually the value from won the series... again it's makes clear it.... minus tax.... plus lawn...............yes...."

Lol

Transcribed audio FTW

[patrickJMT]

@MultiRayKing yes, i must talk in a confusing manner cause google gives my videos crazy transcriptions

[Danasqu]

u r an amazing teacher ! thank u that's really helpful !!!! 5*

[Flaminheartx3]

Shit! My exam is gonna be on this. And it is gonna start in like an hour...Guess I am dead for this -.-''

[TheEirica]

@Flaminheartx3 DON WORRY! you could do it. i never read HS calc books, just watched these vids an hour b4 the test and aced it. ^^

[Flaminheartx3]

@TheEirica Hahah pro :) Thanks god now that I passed the class xD

[TheEirica]

@Flaminheartx3 Congrats! ;) now i wish Pat could do physics as well XD cos that shiz is hard XD

[TheJawsusNSexmanShow]

lol ree-mon sums

[Tobey7049]

wow! I finally understand this! Thank you thank you....I trust you more than my textbook! lol!

[shahzun]

PATRICKJMT SAVED MY LIFE!

[patrickJMT]

@shahzun haahh shirts for everyone!

[c9r0l1n914]

i'll buy one for each day of the year...actually i'll make a religion out of it!

hours and hours reading "calculus..early..blah blah" .....not at all compared with your 15min high quality class! =D love it!

[indyinmink]

Awesome, can't wait for the shirts, i shall wear them to math lecture! and thanks patrickJMT, you really are saving my life right now!

[resistnzisfutl]

You are awesome, thank you so much for taking the time to make these very helpful videos!

[CrackHeadForLife420]

How did people learn calculus before PatrickJMT???

[ddkramerful]

you should make "patrickJMT saved my life" shirts. i'd buy one. maybe three.

[patrickJMT]

@ddkramerful i think i actually am going to make some shirts soon : )

that sounds like a good slogan : )

[TheEirica]

@patrickJMT I'd so buy one of those XD cos it's so true XD

[smirelmi]

you know how u have the formula

Xi* = a + (Δx)i

Xi* is the mid point of the rectangle so isnt it (Xi = a + (Δx)i)?

i also saw this in one of my calculus books thats why i braught it up

[323gus]

when to riemann sums have to be used instead of integration?

[4thKyuubi]

SUBSCRIBED!

I swear, I LOVE EVERYTHING about MATH EXCEPT FOR RIEMANN SUMS. Butttttt, Thank you for explaining gazillion times better than my instructor! I have a test next week and this is like the only lesson i am not getting until i saw your vids.

[robbiegodi]

ur my hero

[glamis400]

Thanks. Let's go lefties!

[kgauc2]

hey just a quick question....why does i=1 in this example?? message or comment back or watever...thanks heaps very helpful!!

[CuMeiLin]

i'm getting nervous about our exam on wednesday.. aarrghhh....

[creemepuff]

LIFE SAVERRRRRR

[Smarkand28]

thank you very much and you are so right they do make you do the whole thing out in calculus, its on my test tomorrow

[harshil200771]

thank you !!! :)

[agtsystem]

cool. this really helped. and yeah usually u learn riemmans sum first as a proof and to estimate the area of n integrals, then u learn by taking anti derivate of f(x), and when that becomes too difficult, u learn the substitution method. i hate math =] <3

[CuddleGlen]

its just a different way of finding the area under the curve within that domain.

this usually comes before the fundamental theorem of calculus, which is an easier way

[goldenguy92]

Would this be used when the equation is hard to anti-derivate. Or is it just used when the prof wants to test our knowledge using it?

[gangster8101]

there's another method called substitution that you normally use when the function is more difficult to take the anti derivative of

[bombombo]

It's just to test your knowledge. Later on you'll be using "regular" integration.

[farshadguitar]

sir, u are my best friend

love ur videos

watching it for all my tests

[Pandahombre]

Patrick it is nice to see you are left handed, just as I am

[erkz]

Pandahombre it is nice to see you are left handed, just as I am

[taypostre]

thank you from chile..

[elisaav]

Heyyy!!! I soooo love your writing!! love those 2 you make :)

ooh, and thank you so much for this video, I have a test tomorrow and this sort of made me feel a little more confident about what I know :) you're great :D

[fizzel89]

this is awesome, patrickJMT...please have my babby...as soon as i find out how babby is formed :(

[fantantasyman]

hello pat, is

Xi* = a + (Δx)i

always true? regardless of using left, right, or midpoint evaluations?

[dfrey483]

yeah i'm wondering that too

[mdogboy0]

im thinking of doing maths at uni, does anyone know any jobs you can gt with maths

[C1u3z]

A teacher? ... lol

[nafnavigator66]

i have seen quite a few of your vids and i honestly believe there is nothing more beautiful than mathematics. unfortunately i will not be taking math after high school, ive heard from many its hard to avoid stress and enjoy math in uni. lol but seriously u are truely awesome and hahaa sorry thats nothing like element oxygens comment :)

[57672b]

thanks~!

[sokkakings]

sorry bro rated it as one accidentally, but favorited it to make up for it..BTW thanks for this video and the rest, without you vids my calc mark would be 20% lower no question.

[mrsbaguette]

you are really awersome! please don't stop making these video .

[aqualizard2991]

this is awesome!!thanks for posting... Do you by any chance have a video with an example where the function goes below the x axis???

[scottturner1994]

I know I already asked you, but how do you get n(n+1)/2 from the sigma notation?

[broli720]

wish u could take my quiz for me man. lol

[matnsas]

T minus 1 hour and 40 minutes until the start of the exam.... ah!!!! no reimann sums on the open response god... just some of that good old trapezoidal rule (have some mercy) ... or even simpsons rule... anything but this, I'm confused :(

[patrickJMT]

yes, this stuff is a bit tricky the first few times around

[matnsas]

there was actually a left reimann sum approximation problem and I think i got it... it was the rest of the open response that was H.A.R.D.

[LukeTennisMofo]

Yeah I am fucking bombing this part of the exam tomorrow...here's hoping for that 45% that will get me a 4.

In all seriousness though, these videos really are the best. And you, sir, are always the man.

[EatthisCHIB]

I was wondering:

for x sub i, is it always (a+delta x) * i?

[patrickJMT]

almost... it would be

a + (delta x)*i

(that is, the i is not distributed to the 'a'.... i assume you mean what i wrote though!)

[cHeryljwanG]

i'm totally going to fail the ap exam.

i'm an asian failure ):

this just goes *wooo* over my head D:

but it cleared a bit of it up at least

[patrickJMT]

it is just a test, and the ap test at that.  to be honest, i would say: who cares! it is really not that important.

[lysolluvswindex]

haha asian failure...that's an oxymoron....yeah well don't worry abou it i'm not asian but i'm probably gonna fail but this is helping a lot thxxxxxxxx!!! xoxo

[HeyWheresKel]

plus, if we do bad on the exam, that just means we'll be better prepared for calculus classes in college! the important thing is we try.

thanks for the help patrick

[superflex007]

I took a weekend to learn this , but then i forgot it again. After seeing this video , i now know it again. Thanks !

[jdbrown371]

Excellent video. I'm going to recommend my physics students to see it. Hi physics students! Also the sum formulas are easy to find elsewhere on the internet and are easily proved by induction. To come up with the original formulas you can use the k^3 - ((k-1)^3 trick found in Spivak.

[champion909]

Thank you