Added: 3 years ago
From: patrickJMT
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  • Came back to review how to change limits of integration when doing U-substitution. This was a quick and simple way to get exactly the information I was looking for. Thanks.

  • @v33nx0r perfect :) i actually now have a video about ' u - substitution , when do i change the limits of integration ' cause so many people aked

  • this was sooooooo helpful! omg thank you:)

  • this video is the oldest out of the ones i watched

  • How did he account for that first x^2 outside the quantity? From what I understand he only substituted the inside? Somebody must know.

  • @IntellectualPopulist I believe he divided the du by 3 and then just plugged the du into the equation, which somehow cancels out like dx does. If that made any sense at all . . . It's around the first minute of the video. You just have to pay close attention to what he's doing

  • That was nice!

    I am just preparing for next term (which starts in a week). I was able to get an A in Calc 1 because of your videos. Figured I would start studying a little earlier because everyone is telling me that calc 2 is SO Much harder than calc 1.

    Do you feel this is true?

    Thanks,

    From Oregon

  • @wperlich integration is typically harder than differentiation, so yes, i think calc 2 is probably a bit more challenging

  • your teaching is one of the clearest I've come across. Please become a math professor and teach at my university!!....we have some really shitty math profs where I am....

  • Ha, I actually spent a few minutes looking for this video! Seeing the giant white board (versus your smaller one or paper) threw me off, heh.

    I'm incredibly grateful for all you do though. Math has always been a bit difficult for me, but everything you've done has made it so much easier...and pleasant! Thank you so much =)

  • @patrickJMT Don't we need to plug x^3+1 back in for "u" to finish out the problem?

  • @TheSrrobinson nevermind I see how this works out. I see how changing the bounds of integration with respect to "u" allows us to not need to plug in the original value for "u". Also, I see that if you keep the bounds the same then one would need to plug in the x^3 + 1 value replacing "u" to finish solving. Eureka!

  • I have a final in 7 hours and have been struggling to grasp this concept for the past two weeks. Thanks to your video I finally get it, thanks a bunch and keep the videos coming!

  • @patrickJMT don't you need to put u back in terms of x after you find the antiderivative? and then evaluate at the limits? like (9^3 + 1)^11 etc... yes? no? god im confused

  • @searching4somewhere i had the same question. If you do not change the bounds of integration then you would need to plug in x^3+1 for 'u'. However, since patrickJMT changed the bounds of integration with respect to 'u', we can simply plug in the new bounds for 'u'. Try doing it both ways, and you will get the same answer.

  • @TheSrrobinson Thanks for clearing that up, I was actually doing some problems today and kind of figured it out on my own. But im probably going to forget how it works anyway lol

  • what happened to "+ C"

  • @eyeheartthekillers you do not need it for definite integrals. i just cancels out when we subtract so people do not bother including it

  • @eyeheartthekillers

    It's a definite Integral, which is an exact value, so no +c is necessary.

  • U=awesome(x)

    dU=totallyawesome(dx)

  • You are a lifesaver!! Thank you so much for taking the time to share your knowledge, for free! :)

  • Thank you so much!

  • you saved my ass so many times 

  • thank you so so so so so so much! i learned more in an hour watching your videos than a whole month in my calc teacher's lectures...

    and i think you're much better than khan academy :)

  • You're amazing, your videos are the only ones I've found (after searching for a good amount of time) that have really connected the topics for me. Thank you =)

  • @Sharylyn13 come back and watch any time ; )

  • @patrickJMT wat a playa lol

  • I did think that you had to include the Constant of Integration but I didn't think you had to since you had a definite answer? (Is that the right term or? Not sure =/ )

    Since our answer is 186 there is no + C right? maybe?

    By the way I'm only 14 so I was just wondering if what I did was right =)

    Please reply if you can? =)

    Thanks =)

  • Hey PatricJMT - I have a question that would be nice if you could answer:

    When you write out the equation with integration and expansion, How do you continue to break the equation down? - For example

    [Int - 0 -> 3] 2x (x^3 + 4) dx

    I understand that with 'U' substitution you replace (x^3 + 4) with U right - but do you just cancel out the equation and do this? :

    2x^4 + 8x du ?

    and then

    186 - 0 ?

    with the resulting answer being 186? - And you don't take away anything as 2x0^4 + 8x0 = 0?

  • You're a great teacher. :)) Thanks!

  • thanks

  • you just got another subscriber, thanks much!

  • I want to sex your face right now....this video just saved my grade on my quiz

  • boo mormon commercials

  • u r my hero 

  • @KoreaXFan

    You would if you weren't looking for area. Of it's a definite integral, you can leave your variables in "u" and plug in those bounds.

    You CAN go back to x's by subbing in the x^3+1 for u, but you would have to change your bounds back to 1 and 2, so it's easier to leave it in u's for definite integrals and you get the same answer.

  • oh man i wish i had discovered these videos earlier in the school year.... they would have saved me a LOT of stress

  • Calculus is fun

    ONLY if u know wut the hell to do

  • good vid but i reckon you should teach the derivative outside theorum! e.g. the 1/(n+1)f(x)^(n+1)

  • At the end of the video don't you first place back in the u = x^3 + 1, then you add in the 9 and 2?

  • This was EXTREMELY helpful, Thank you so so so much

  • You're the Jesus of Calculus

  • dude, god bless ya , you are the man , i love that you use short cuts and you make your videos as short and as informative as possible , i don't know but some teachers talk maths like it is symbols or something , they keep saying things like (if and only if , let R>>>C ) and such nonsense and i think it turns many people off from the beautiful world of math.

  • Seriously man, I love you. Straightforward, easy to follow, and I don't fall asleep, which is way more than I can say about my calculus class.

  • can i ask why do we need a new limit when we integrated it and the limit 1 to 2 is no longer valid? thank you so much

  • Comment removed

  • you make my calculus professor look like a genetically mutated Neanderthal

  • would the answer to the u-substituted part of the integration be multiplied by the integration of the x^2,x,1,2?

  • is it okay if i say that they way you teach is oh so magical? omg xD

  • omg sooo helpful

  • Dude his arms are so veiny and kind of muscular *giggles*

  • I LOVE YOU.

  • has anyone ever seen his face?

  • @MrMig3 I think the background of his Channel has a picture of him. Lol, you can see his face there?

  • Your videos have been very helpful for my Calculus class. I have one question. Can you tell me why in the first example the limits of integration are 1 and 2 are no longer valid. Is it because its 1/3 du that is equal to x^2dx? Thanks!

  • this is great!!!!! XD thank u!!

  • Thumbs up

  • You just made my life so much easier XD

  • Comment removed

  • I'm a 2nd year university student who was working on some first year math review. Thanks to your tutorial, I am now able to understand how to do u substitution with definite integrals ! :D

  • I don't know what 9^11 is, maybe you do... love the subtle humor

  • my ass is saved! Thank you so much as always, I can't believe the wealth of knowledge that you have on here...I wish I would have found out about your vids during calc 1....there are others, but the way you explain things is so comfortable and easy to listen to and understand.  I bet you make a hell of a teacher!

  • You saved my ass in calc I, thank u very much

  • 3hours of trying to figure this out just figure it out in 4:47 because of you..thank you

  • u r gr8 !!!! thnx ..

  • Love your video, I like the HD ones more :) but everything great, even your voice is nice to listen to.. I got a calculus final tomorrow, and I feel a lot more comfortable after watching your videos.

    Thank you so much

  • @eoterm yes, this was one of the very first videos i made - no HD camera at that time : )

  • @patrickJMT With definite integrals can you just plug the original value for U back in and then solve using the original limits without having to calculate the new values limits for the U integral?

  • @IGNsucks yep!

  • @eoterm I've watched his vids before all of my calc tests and have made As on all of them so far lol. Pretty good considering i go to calc maybe once a week.

  • @eoterm can someone please tell me why it is so useful learn calculus fro real life apllications

    when will it come in handy?

  • i was wondering in what age does integration being teach to students in US?

    in my country it was 17 . some one answering?

  • This series on integration filled in all the pieces that I didn't get in lectures. Thank you for your time preparing these.

  • Patrick, thanks so much man, it's 3am here in AZ and I've been up all night studying for my calc 1 final. You've helped so much! hopefully i get above an 85 (which is what i need to sustain my A)!!

  • @resevil787 i assume the final was today... i hope it went well!

  • @patrickJMT yessir, got an 86, which kept me at a 90 for the semester. Thanks again man!

  • You just saved me! (As always!) :) Thanks a million

  • Haha I don't think too many people do know what 9^11 is off the top of their head. Daniel Tammet probably does though. If you don't know who he is search "The boy with the incredible brain" on youtube.

  • thanks for the video. you make it seem so easy

  • I was very sick and missed a good deal of time at school. An hour ago, I was in tears because none of my classmates take notes or care about calc, so I was in trouble. Thank-you so much! You really help out the people who try in class and want to work hard, and you help the people who need a different method of learning calculus than what their teachers may teach. God bless you!

  • @8WingedAngel khanacademy is another good online teacher.

  • you saved ass for my test tomorrow, thanks buddy!

  • Again, you have shed light on a concept that seemed complicated. However, with you my friend, nothing is complicated. Thank you.

  • Thumbs up! Thank you for taking the time to explain this so clearly.

  • You are an awesome person. I like your videos.

  • sry but if u is x^3 then u´ is 3x^2.

    so you have to multiple the integral with 3 not with 1/3 or not???

  • do you always change the limits everytime you use u-sub?

  • you are so cute patrick

  • 1:26

    I like your spin technique it somehow helped

  • Comment removed

  • This is way better than reading explanations from a book

  • thanks sir these are very helpful for us. i am learning calculus from ur videos

  • Ehm how do you do (9)^11 without a calculator lolz

  • @Aaroenz0r 9*9*9*9*9*9*9*9*9*9*9... Just do long multiplication. Old school elementary style. =P

  • why didn't I find this channel 2 years ago? my math problems would have disappeared by now.

    Great videos; you do it better than all of my teachers. I have some grade raising to do!

  • i think criticism is humbling. unfortunately, there is never anything to complain about with these videos. but this time, i have noticed something. i prefer paper to white board. lol. there, i said it. i found something i actually would change. besides that, its perfect. keep it up! for my education's sake.

  • well, i prefer paper actually too, but it seems so wasteful

  • Just recycle, and your videos are gold! =]

  • @patrickJMT

    yea...i was gonna ask you sometime where you get all of your paper from...because you go through so much just making these vids, lol.

    I too prefer the paper or the tiny white board that you use, instead of this bigger white board....it just makes it seem like you are a tutor that's helping me 1 on 1, instead of the teacher showing the whole class.

    Apart from that, there's nothing else to complain about; your videos are always very helpful

  • thank you very very much...

  • ur smart

  • You are the man! I am wondering why the limits of integration 1 to 2 are no longer valid when using u's in this problem? Is this always the case or just in this example?

    Thanks for your help.. Your videos rock!

  • brother note that limit of integration are changed in all definit integal substitution while it remain same in the indefinit integral subsitution method

  • i would like to see [integral sign pie =b 0=a (sin(x)+cos(2x))dx] im stuck on that problem

    or is there a video that already addresses that?

  • I think you're antiderivative is -cosx + (sin 2x)/2

  • your better than my calculus teacher

  • amen

  • his better then all our calculus teacher lol i don't eeven know wat topic were doing in our class

  • @luisr12491 yeah i would agree

  • Thanks for the video. It helped me on my homework.

  • so once you change your limits with respect to 'u' you can just plug those limits in for 'u'? i might be wrong but i remember being taught that you can keep the same limits and then just plug the original equation that contained x in it for u, and then evaluate your anti-derivative at your original limits... does that work too?

  • Fantastic explanation of u-substitution for definite integrals. Thanks so much for taking the time to post something like this on YouTube to help us all. Your explanation was clear and easy to follow, and the added complexity of the 1/3 term really helped clarify how useful u-substitution can be even when the derivative of the u term doesn't appear exactly in the formula.

  • great* even

  • your a lefty too :P grat vid btw. covers u subbing well

  • THANK YOU for your videos!!!!!!!!!

  • I LOVE YOU.

  • Thankyou VERY much for your help. Your explanations were very clear and have solved alot of my integration problems! It feels like a door to the harder questions has been opened up!

    Im not as worried for tomorrows exam anymore =D Whooo!

  • I like that you included the new limits-that mistake cost me 2 points on a midterm.

  • Well explained. Thanks!

  • im really confused as to where the 1/3 came from and where the x^2 went ?

  • the 1/3 comes because We're no longer defining this function in terms of "x" but in terms of a different variable "u". However, in order for the two expressions to remain equal, we need to alter some of the integral's expressions, otherwise our substitution is quite pointless.

    the 1/3 just comes because he distributed it out of the expression as what was formerly x2 dx, then became 1/3 du.

  • since he had a x^2 and a dx in da original equation. he minipulated du=3x^2.dx using algebra so he got 1/3du=x^2.dx. he just divided both sides by 3. so he gt x^2.dx on the r.h.s. he just replaced the x^2.dx by 1/3du in the original equation. does that make sense??? lol

  • man both sides are divided by 3. and then when integrating he factored it out, because it is a constant. man look what he did in blue to know what happed to x^2, it is replaced by du.

  • thanks alot for the video, but it could be done without having to look for a new limits. its even more complicated trying to look for a new limits. thnx:)

  • well, eventually, when one starts doing multiple substitutions or multiple integrals, it is easier to find new limits as you go, so one needs to see it in order to do those problems!!

  • This took my teacher a week to explain. I just got it in a few minutes...THANK YOU!!!

  • thanks so much. my math teacher is horrible at explaining things in understandable terms and you're so good at it. Thanks for the help!

  • What's the difference in calculating the new limits before as opposed to just putting the old limits back in later. So after intergrating .. your equation would be:

    1/3 * (x^3 + 1)^11 / 11 .... if you plug in 2 and 1 as x now ... you'll get 9 and 2 ... that's the exact same thing. I don't get the need for finding new limits ahead of time.

  • You're absolutely right. You can do one or the other, like a previous comment says. Changing the limits of integration just makes it so you don't have to change u back to what it was before. But if you change u back, you can leave the limits of integration alone. Do one or the other, whichever you prefer.

  • OK, still my question is Where did the 3x^2 come from???? Why did he choose 3??? Will always choose 3?? Or can a just pull a number out of the clear blue yonder??? I see everything else in the problem except where on earth the 3 comes from????

  • 3x^2 is the derivative of ( x^3 + 1) .....bring down the power infront of x and then subtract 1 from the top...... hope your familiar with it

  • 3x^(2) came from the derivative from the x^(3)+1 term, which is = u.

  • 3x^2 is du

    u is x^3+1 so du/dx is the derivative of that,

    manipulating that gives du=3x^2 dx

    he just moved the dx to the other side

  • 3x^2 is the derivative of u=x^3

  • 3x^2 is the derivative of (x^3 + 1).

  • OMG!! Thank you Thank you Thank you Thank you Thank you Thank you Thank you!!!!! This is great. The best on youtube by far.

  • thank you VERY much.. you are a life saver.. i really appreciate your videos.. thanks again

  • Mr Patrick is know his stufffffff.

  • yeah, can someone please explain to me why you don't plug in ( x^3 + 1) back into the fxn?

    btw, you're awesome! this is the first day i watched ur vids, and i get everything =]

    ive watched like 3 so far

  • when you let "u"= "something", that "something" has to be pluged in to u

    after when you take the integral.if you don't, you are just taking the integral of u, not the integral of that funtion. So, the function has to be pluged in to U.

  • but he changed the x from 1-2 to 2-9.

  • u no how first his got like 1-2 for the x, then he changed it to 2-9....its because he already put in that equation for the new numbers, so thats y he didnt plug in the equation in the end. You can do one or the other!

  • oooh cool =]

  • do you have a video regarding def. integrals using Wallis' formula?

  • i actually understand it better! but i still feel stupid in class yay...

    no but really this helps a lot thank you

  • This is amazing!! Your videos are soo hepful!! thank you sooooo much!!! Youtube isn't just full of random stupidity now.

  • one question... after you integrate and get u^11/33, why don't you plug in x^3+1 for u. I'm wondering, is it because the derivative is with respect to du, not dx?

  • nice muscles in the end lol

  • lol, was i flexing? : ) i am soooooo jacked

  • With an internet teacher like you who needs to go to classes?? 5*

  • glad you like them and... go to class!! : )

  • I started studying for my calculus 1 exam on 1/1/2009 just by watching all your videos about integration and series without having any classes at all! Yesterday i did the exam... guess what? I think it went really well!! I recommend your channel to all my friends who are having difficulties with calculus ;)

    Thanks for everything!

  • Great!

  • lets give patrick the props he deserves - rate his vids!

  • thanks

  • quick question, once you have your U after taking the anti-derivative, couldnt you just plug back in what U was in terms of X and then evaluate it at the old lower and upper limits of integration rather than finding new ones as that is what I'm taught to do

  • yes, absolutely you can do that!!

  • coo sweet vid

  • i was gona ask the same question.. but you already asked and he answered already! great video

  • Nevermind, same thing, just throw the whole thing together, NICE ONE, YOU'VE SAVED ME!!

  • PURE OWNAGE, what I needed, the dang change in limits after a u substitution, one problem... is there an example with changing to trigo? the limits will have to change to angles... which may pose difficulties for certain questions...

  • Great stuff, thanks

  • wow nice and clear explanation, thanks!

  • I'm a math prof and I appreciate the care with which you explain the process. I even gave a link for this to my class of biology majors for a well-worked out example with good tips too.

  • thanks for the kind words! i always appreciate hearing from a fellow teacher.

  • : ) i am glad that my explanations help! i try to keep things as simple as possible!

  • I took this stuff about a month ago and your explanation is so easy and helpul. All the instructors I get love to RUSH and make it so hard when its not. So basically what I'm saying is, I wish my instructors taught like you. Maybe you should give them a lesson.

  • Thank you

  • Thank you so much your video is so helpful

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