Calculating a Definite Integral Using Riemann Sums - Part 2

[BitchOnDaFloor]

yea big thanks from germany

[sockmonkey1983]

OMG this saved me for my university calculus midterm!!! thank you!

[Sledgehammerguy]

great/clear video

[TheOnlyBERT67]

I wish my professor would just explain it like this! Thank you for taking the time to make these videos.

[patrickJMT]

@TheOnlyBERT67 no problem, happy to help

[iPodAppsWeekly]

thanks so much!

[Alexville]

Thanks a lot Pat. You are amazing.

[St3v3n947]

thank god for patrick JMT

[jessiesun1142]

my math professor uses your video to explain things...

[patrickJMT]

@jessiesun1142 ha! tell him / her that i said thanks for using my stuff!

[MIMIFRENZY]

@jessiesun1142 I wish my teacher would use his videos. My teacher just breezes through everything, doesn't really take time to explain anything. So frustrating!

[RealXbody]

Great thank you!!!

[lollipop623]

The simple problems are great because it helps teach the concept of these techniques but can you show some more complex problems as well?

My teacher tends to use problems that don't simplify as easily.. or maybe i just don't know how to do it..

[franknguyen007]

Thanks alot... Keep it up...

[M1lkY1000]

Really thanks alot... this video is very useful(=

[Wsmstng08]

u just saved my butt in calc

[tndas1493]

Much appreciated! I'm in Math 221 (Calc 1) at UW Madison and my professor glossed over this and we were stuck not knowing how to do it. Thanks a ton!

[arsenalgooner01]

LIFE SAVER!



[loserdude101]

You rock!

[BillieBaby143]

What if the exact value of delta x is given, say 3...can we still do it this way?

[AdorableMacky]

@BillieBaby143 Delta X is equal to b-a / n u know. Mostly in such problems, esp on lower/upper riemann sum questions, n is given. So with n known, u know delta X and still use this concept.

[BillieBaby143]

Finals week; time to look through your notes!

[thatchickslara]

Thanks for these kinds of videos. They really help :D

[SardarOnTop]

God bless you sir.

You are doing a very good deed.

[Prisquared]

thanks for your vids!

[ikkinnikk]

lawd...

[linabear55]

you are so great. these videos are getting me through university calculus haha

[tckelly38]

"I'm not lazy... just clever." my new go to phrase!

[Crossoverzz]

@tckelly38 such a good line

[rohailwasim]

Thank You ! Now I can probably pass my Calculus 1 exam :D

[insidedreams88]

Thank you very much. God bless you!

[marangiop93]

when you have limits at infinity and you have a rational function but if the degrees of numerator and the denominator are different , what happens then?

[Angelgrrl04]

@Kenikozo - What's math engineering?

[kenikozo]

I hope you also cover concepts from 2nd, 3rd and 4th engineer math (I am in my first year -math100- and these tutorials are very useful!)

[FeelingFreshSon]

and the epic conclusion...thanks!

[barbaric37]

I spent so much time going through this dumb concept in my book and I was so confused! but you cleared it up and helped me solve my problem, thanks!

[patrickJMT]

@barbaric37 come back any time! : )

[GoodyearBandit]

@patrickJMT lol patrick, wish me luck buddy passing this class :)

thanks for the help. without out you 85917 students were lost...

[maywong2012]

very good!!!!

[pabs123]

i dont understand what you start doing at 3:18

[maxlinkmax]

@pabs123 he is using the formulas he introduced at the beginning of part 1 to make the whole equation can be solved by taking the limits toward infinity~ and those formulas are just the kind of formulas "u just have to memorize them" in calculus... like u just have to memorize the quadratic equation for ur pre-calc course. hope this helped

[7l00l]

THANK YOU !!

THANK YOU !!

THANK YOU !!

THANK YOU !!

LIKED + SUBSCRIBED

[midnightpanda]

You've become a integral part of my math experience.

[riceluvnflip]

Reimann Sums are stupid :(

[Ammoniummetavanadate]

All I have to say is that it is 3am, my assignment is due in 5 hours, I did not get the question at all, and then I watched this video.

In short I love you.

[xviperzero]

can you be my prof?

[CindyDIK]

is there a video about calculating from i-1?

I know the result will be the same as calculating from i, but our class requires us to do both...

[HeliosFire9ll]

what if there was only a constant, lets say an 8 rather than X^2+X+1

[allanahk56]

You are a legend. Super helpful for my exam in 3 hours!

[paigelizabeth11]

What if you get an i^3?



[patrickJMT]

@paigelizabeth11 you'll have to find a formula for it!

[nlrush248]

@patrickJMT the formula for that is: (n^2(n+1)^2)/4 ....... so it is like you square each component from the first formula.

[penderrin909]

@paigelizabeth11 the sum of i^3 = ((n(n+1))/2)^2

[lfcforever]

@paigelizabeth11 if that happens ,,, you will just have to get an i^pod

[alexcandy1411]

@paigelizabeth11 It is [(n(n+1)/2]^2

[froggaman123]

@paigelizabeth11 (n^2(n+1)^2)/4=i^3

[BillieBaby143]

@paigelizabeth11 i^3 = [(n(n+1))/2]^2...Sorry I'm late

[0xXRaquelXx0]

@paigelizabeth11 (n^2(n+1)^2)/4

[naytus]

great job

[patrickJMT]

@naytus thank ya

[JLchevz]

Wow that was pretty good :D thank you for posting this

[Beaglier]

thank you for the instructional videos. they have helped alot.

[rHaiKu]

thank you so much!!! i couldn't understand the book.. this has helped me a lot! :D

[halflife1994]

is there a short cut? =)

[Mlejayne]

Thank you! You're better than "Idiot's Guide to Calculus" and "The Calculus Lifesaver," not to mention my textbook.

[ash1soccer]

Thank you for this. I am in highschool, and I am taking Calc 1 and Calc 2 this summer. Because I am taking them online I am not able to ask the professors any questions. I understand derivatives, indefinite integrals and antiderivatives conceptually and mathematical. However, I haven't been able to understand how to obtain a definite integral mathematically without using the shortcuts. This has really helped me, so thank you very much!! :)

[patrickjohn84]

This guy kicks ass.

[ilovetvb]

THANK YOUUUUUU

[ediyakobov]

Part 1 and two well donee I liked it

Thankxx Patrick

[josephtanaya]

hi patrick, i have a question. it is (a+ delta x i) if it is right hand point. it is (a+ delta x (i-1)) if it is left hand point. what is it for mid point? thanks

[Onizcc]

@josephtanaya if youre trying to find f(xi*) then its simply just ( a + delta x * i )

the xi*th represents all midpoints within the interval.

[Adrury1771]

please keep it up. college calc would kill me this quarter if you didnt have these

[tomyo669]

what do you do if the exponents don't match

[JoNnYShizzle]

I wish my calculus teacher taught as well as you did holy shit.

[adarsh376]

thank you.

[xLACKOSx]

Thank god for the first fundemental theorem of calculus, think physicists would have given up on everything if they had to do this everytime

[xLACKOSx]

Thank god for the first fundemental theorem of calculus

[ChaseGZ100]

Hey, thanks a lot for the video. I only have one doubt, do you have some theory videos? like, where do you get the equivalence of i ? (i haven't checked the rest of your videos, so excuse me if the theoretical explanations are there)

[Crossoverzz]

Forget this man's heavenly teaching, he is writing on a white board LEFT HANDED.

[iRockNRolla28]

Are Riemann sums always this tedious? Is there anyway of working them out pictorially?

[blakelawdix]

You are a saint.

[DTTRIX]

This video has been life saving!

[lphiljipl]

funny how many bad teachers schools have and good teachers youtube has :p

[joser590]

You lost me at 5:40

[Meephouse]

This sh*t is fuc*ing HARD.  Jesus take the WHEEL. Thank you for the video though... I still gotta re watch it.

[ThePassionateAsian]

So what if the numerator and denominator's exponent is not the same? would you still take the ratio of the coefficient? 

[patrickJMT]

@ThePassionateAsian no.

[ThePassionateAsian]

@patrickJMT can you show an example where the exponent is not alike?

[kirlia281]

@ThePassionateAsian ok so the trick is if the numerator degree is higher than the denominator, the limit will go to + or - infinity. if the DENOMINATOR is bigger then it will go to 0 so it cancels out! =) then if they are equal it is the ratio of the coefficients! hope this helped!

[ThePassionateAsian]

@kirlia281 thanks :D

[imthelittlesealgirl]

@patrickJMT than what would you do

[ash1soccer]

@ThePassionateAsian In this case what happens depends on whether the numerator or denominator has a larger exponent. If the numerator has a larger exponent then the function would approach infinity, and if the denominator has a larger exponent the function would approach zero.

[mmoser2010]

P.S- GO BUCKS!

[mmoser2010]

you got me an A in calculus 1 and im moving on to calculus 2! thanks for all your videos

[Purplecobrafan]

10 people still can't do math lol

[Rockwell84]

Just wanted to check, at 7:25 I think you meant to say you are adding those first 2 terms right?

[coooldonkey]

thank you SO MUCH, i finally understood. My math textbook is so absolutely terrible at explaining anything to anyone who do not already understand the problem is ridiculous. Aww will its to be expected since a professor at our school did write the book. Sick of our university doing that, if we actually get a teacher like you maybe half of my class won't fail math.

[ali3ncas3]

Thank you so much, I missed a couple days of AP Calc. and couldn't figure out how they were doing theses based on my friend's notes, but you made it really easy to understand.

Also,do you have a video on how to do this with the "short cut" using anti-derivatives?

[xwhales]

Thank you so much! I seriously did not understand a thing when my teacher was trying to go over this.

[kashmiri92]

seriously, thank you. you are making such a difference.

Any plans of moving to Canada and teaching here? :P

[patrickJMT]

@kashmiri92 not at the moment : )  however, maybe if enough stupid people vote for sarah palin...

[adv1k]

@patrickJMT

you sound like a fracking genius bro, keep being awesome.

[n0nstiff]

@patrickJMT HA! YOU ARE TOO FUNNY SIR

[tupacsomething69]

@patrickJMT "maybe if enough stupid people vote for sarah palin..." hahahha mathmetician and comedian

[acdcgibsonmaniac]

@patrickJMT

there are a lot of stupid and retarded people in Croatia..............We need you ASAP!!!!!!!!!!

[alannamoss]

unfortunately my teacher is HORRIBLE at explaining things in calculus. thank you so much for posting your videos...without them i would be beyond lost. :D

[patrickJMT]

@alannamoss spread the word

[liztothemax99]

you just made my LIFE with this video!!!!

[wesrightnow]

Thank you for posting this, you're a life saver dudeman!

[atomicfantom]

this is by far the best video lesson I've ever seen and in just the short duration of the videos, I learned everything I needed to to know about this pain in the ass process

[loik345]

Thanks Patrick. I am surviving calculus 2 because of u. God Bless u man.

[kiyotewolf]

ahhhh.. my eyes they burn.. with math!!!

[apalahubog]

Thank you

[essential181]

I just couldn't make sense of the book on this one. Thanks for posting!

[sjbuccy]

What is the rule/theorem called where if the polynomials have the same degree in a rational function, the limit as x approaches infinity is equal to the ratio of coefficients? Great video and great explanation, Im sure we all wish you were our instructor.

[RRadRussian]

Thank you for making this video!

[r2s112]

On the last part you said 2 times 2 equals 4, but you have an addition sign???

[kennzygh]

Thank you once again , i was totally lost in class, but u just saved my day. thank you.

[trescontente]

thank you so much for this. i have my calculus final tomorrow and my lecture professor never explained definite integrals and reimann sums well. i was freaking out until i saw this video! something that i spent two hours on my own trying to understand from my textbook, you helped me understand in around 15 minutes. thank you for such a clear and concise explanation! i appreciate it :)

[mas3rm1nd]

I hate how my teacher is making us do this on the test...

this method is so long and tedious and POINTLESS

great video though, much clearer now :)

[RRadRussian]

@mas3rm1nd But how about cases where you cannot find an antiderivative of a function? w/o calculator of course.

[Cuzipwnlikethat]

Amazingly clear. I have a test tomorrow and you helped me realize that I've been doing Riemann Sums horribly wrong. Thank you for clarifying, I greatly appreciate the not C that I will achieve with your teaching. :)

[XxImmortalmagexX]

amazing video

[Kybabiee]

so i'm currently in AP calculus, and we just started integrals last week but i was already worried about my understanding. however, thanks to your videos i'm all goood now! so thaank youu very much for your super easy to understand vids! i love your method of teaching, and the different coloured whiteboard markers and it's just... perfect! :) you're my study secret! ;)

[josephtanaya]

very nicely explained! good job!

[D41ryQueen]

goddamn it I have a test on this in 6 hours and we aren't allowed to use the anti derivative method T_T

[xrockerchick4lifex]

Omg you are amazing! I spent an hour trying to figure this out on my own, but I got it watching your video in 5mins! Thanks soo much!

[dillster31v]

Why can't you be my teacher??

[cukie7707]

Thank-you so much you have really helped me and now i understand how to do these types of problems! :D

[elenitino]

Thank God! Now I know how to do my homework. You really helped :)

[powerbrea27th]

yo Patrick you just help me out men i subscribed to you and this is best decision i have made you have really help me understand this stuff better. May you live long

[Brady580]

Thanks, this was really helpful.

[u18db9]

Wow...you truly deserve all those good comments out there!....

[MissKierie99]

I love you ^o^

[Pooh0Bear8]

Thank You, Patrick

You are a life saver

[niallcello]

thanks for this video. the concept really clicked after watching it. your explanation is very thorough and clear.

[Ascully]

can you do this with only a table of values, by that I mean with out a function given

[bwari01]

I love the "tricks" coz they eliminate too much algebra that could lead to mistakes. Thank for this video.

[sanzo21]

its so ironic how the teachers we PAY teach like SHIT, while GODS like mr patrick over here enlighten us by (WAAAAAAAAAAAAAY BETTER) ^infinity for free. THANKS SIR YOU ARE A GENIUS, AND A REAL BLESSING FOR STRUGGLING PPL LIKE US.

[j435ung]

How would you do that problem if the partitions were not equal on [1,3]?

[samah674]

thank you so much for this video. i thought i will never be able to solve such problems.

[eoterm]

I been trying to understand this for the longest time, and now its all clear, thanks!

[Zyntle]

wow thanx my lecturer made dis difficult

[patrickJMT]

@Zyntle well, i would say most people find it a bit tricky the first time they see it. just a lot of formulas and little details to remember.

[Khedr91]

@Zyntle ya i know what u mean, its waaaaay simpler than when lecturers say it

[aztecatenocx]

You just made my day. You explained this very clearly and explained how you did certain parts.

Wish you were my instructor

[patrickJMT]

@aztecatenocx if you watch my videos... i am : )

[spirite22]

@patrickJMT We are proud you are :D

[manda1shorty]

Thanks so much the video helped a lot thanks for taken the time to post this

[prchick23]

Thank you so much! I'm taking calculus and I did not understand my professor. You're great!

[zeekkay]

Very helpful, especially that limit trick at the end where you can skip out on some of the grinding. It's very easy to forget that one.

[morales7vera]

great, you are a machine

[keviniaobees]

thanks heaps bro your the man

[ran6257260]

This is reall helpful. Thank You :)

[ran6257260]

this is very helpful. Thank You :)

[jesuslover037]

Wow, you were right; this is the longest problem ever.

[fractalification]

Thanks man, there's a special place reserved for you in heaven.

[coolfun74]

awesome

[walkingpunk]

isn't this too hard?

[JohnNumberThree]

So, I feel a little dim-witted asking this, but, the formulas you get for the summations of i and i^2, those are derived by taylor/maclaurin series right? Excellent work by the way. I've had two semesters of calc already, but they were taught by a truly rigorous professor who, although displaying a thorough knowledge of his field, I think expected to much out of his students. You do an excellent job of bringing all of this down to an earthly level.

[TheMistercrowley]

lifesaver man

[Theincapower]

what can I say? ... Thank you!!!

[TheEnglishRogue]

wow. i spent two hours today trying to figure this concept out. After 10 min of watching your video, I got the right answers. Thank you

[Lunibell]

Thanks a lot! You saved my calculus exam!

[linkmarche]

"Not lazy, just clever.".... so true xD

[kgbmonthly117]

Dear Patrick,

You have been my go to guy for math instruction for 2 semesters running. I got an A in Precalc and So far an A- in calc (hoping for the A).

I am wondering about whether or not to go ahead and take calc II.

I am a biology major (premed) and I am wondering what awaits me in calc II. Any thoughts?

Also, expect a small contribution from me, since I really appreciate your work.

Thanks very much and I hope to hear back from you.

[rawrdinosaur18]

i wish you were my math professor...he takes math to a psychotic level where it makes no sense at all to a class of engineering students

nice video!

[loveling1224]

@rawrdinosaur18

hah, your comment just reminds me of my math professor.

[bleachedbutterfly]

omg.I  love u patrickjmt

[ishotyaaa]

haha i was paying so much attension, i noticed the slightest verbal mistake on 7:27 lol.. fucking sexy video though :)

[ishotyaaa]

lucky however it worked out ^_^

[dgizowski]

Thx so much. I'm taking my calc course "online" and am really left with just my brain and my textbook. I've loved your videos that seem to simply explain what looks like greek (literally) in the book.

[patrickJMT]

@dgizowski just say 'no' to online math classes.

without fail, they suck.

[dgizowski]

@patrickJMT Fortunately, I'm gainfully employed. But it's a day job - full time- so, that leaves little availability for LIVE classes. If you find online courses that use "Course Compass" along with the text, they're surprisingly great. My current one doesn't use it. But hey, I would have never found your site otherwise! Calc II is in the fall. Here's crossing my fingers. Thanks again for all the work you've put in.