You just saved me another panic headache. You explain things so well, even my engineer of a father recommended you over his own explanations. Thanks a lot!
He explains so well in so little time. I love the excercises at the end because it helps me review what you taught and makes me more confident in what I learnt.
my new study method is watching 10min youtube videos before reading my text book. Idk how they do it, but each and every teacher/text book manages to make me super confused and make everything harder than it actually is. Thank you for your service prof Dave!
You can learn all high school, college math within a year by giving yourself a reason to do it for, since the brain is evolved to do certain tasks, for survival and reproduction. Save yourself a lot of time and money by doing AP exams way earlier, screw the norm brother.
Thanks a lot!!! I usually have no problem in maths but for some reason I simply wasn't able to wrap my head around integration by substitution. This really cleared things for me and lifted a huge burden!!
Dear Dr. Dave, I would hereby like to submit a humble request for your consideration of the production of an additional calculus video, U-Substitution of Definite Integrals. There's some extra thinking involved, and I would love to see your 5-10 minute take on it. Thanks for all the amazingly helpful content!
Do you have any advice for me learning calculus like in the video? I’m in high school and not doing too well :( . It’s hard for me as I have to juggle many subjects.
What is the video in this series that is where Dave justifies the splitting of dx from d/dx to be able to "multiply" the integrand by dx to get 2x dx = du?
I'm sorry, I know this is said often but... holy cow. This man is up here explaining things that, a year ago, I would have understood about as well as Einstein's Field equations and yet I'm understanding it. The crazy thing is that even though it still sounds nerdy af (which is something I always used to appreciate, but wasn't really able to properly replicate due to a lack of understanding), it's not just going in one ear and out the other. Now I'm not gonna say that it's solely Dave or even just solely UA-cam, but between last year and this year I went from failing at properly comprehending Pre-calc class to sucking in information on Calculus and planning on taking an exam to skip taking the first class all together, and I feel like it wouldn't be possible at *_nearly_* the speed it happened without UA-cam and Dave more than many. I could even say even Khan Academy hasn't helped as much. Thank you, Professor Dave. I first came here for anti-conspiracy content... but I subbed for this.
THANK YOU THANK YOU THANK YOU‼️‼️‼️‼️ i cant believe that all of my questions abt the substitution rule have been answered with a short, 10 minute video!!! THANK YOU‼️‼️‼️
Hey so is it possible if you have an extremely long polynomial, that you can use the Subsitution method in two places in the polynomial at once? So if you had like two sets of parenthesis in a long poloynomial, could you substitute one for U and another for Y (random variable), and then do this method for these two different substitutions at the same time?
Is the point in the substitution rule to simplify the equation? Cause if so i dont really see it it just makes everything more complicated than it already was. Either way, great video 👍👍
If it's my choice, I leave the limits of integration alone when doing u-substitution, and translate it back to the original variable of integration, before applying limits. Some integrals are not possible to do in closed-form as indefinite integrals, so that is the rare times when I opt to translate the limits to the u-world. For instance, the Gaussian integral.
I need someone to write the content, since I never went that far in math myself, I tapped out after linear algebra. If you think you're up for it shoot me an email!
It's called "U-substitution", because it is common to use U as the temporary variable for it. I prefer to use W instead of U, when both integration by parts and U-substitution are part of the same problem. It is not the same thing as algebraic substitution, but the term substitution means the same thing in both of these terms. Ultimately what it means, is if you can recognize an integrand that is likely the result of a differentiation through the chain rule, then you can switch the variable of integration, to a variable that represents the inside of a function. Suppose your integrand is a product of g'(x), and the composition of functions f(g(x)). The g'(x) term might not strictly be the derivative of g(x), but rather you might have to multiply by a constant to get g'(x). In that case, you multiply by 1 in a fancy way, as a constant divided by itself. Part of that ratio becomes the constant you need in order to complete g'(x) to be, and the other part of that ratio, becomes a leading constant of the entire integral, that you pull out in front.
thank you for the excellent explanation !! i'd like to ask, with respect to the first trig example : "sin^6xcosx" why did you choose sin instead of cos, and in an exam how would i know which one to choose ?
if you choose cosx, then the integration proceeds as follows: ∫ sin^6(x)cosx dx u = cosx, du = -sinx dx -> dx = du / -sinx substitute u and du: ∫ (sin^6(x) u du) / -sinx = - ∫ sin^5(x) u du you can see here that x is still involved in the integrand even after u substitution, so this doesn't really accomplish anything. generally when picking u values for trig functions, you want to pick the function whose derivative is in the integrand and will disappear after u substitution. this is so that the resulting integral will be nice and clean and convenient to evaluate
I watched a 30 min long video on yt... Not gonna take his name... And I was completely lost I couldn't understand a shit And then i stumbled upon ur video... Seriously everything is easy now... A bad teacher can make u feel dumb.. really Thanks dude for telling me the correct path when I got lost with that random youtuber
Professor Dave is the teacher you always wanted but never had. Thank you, Professor Dave. You have saved me multiple times.
I have a great teacher soooo...
+1
You just saved me another panic headache. You explain things so well, even my engineer of a father recommended you over his own explanations. Thanks a lot!
There is a simple way to understand science.. Just take your phone/pc --> youtube --> Professor dave explains.. that's all
He explains so well in so little time. I love the excercises at the end because it helps me review what you taught and makes me more confident in what I learnt.
my new study method is watching 10min youtube videos before reading my text book. Idk how they do it, but each and every teacher/text book manages to make me super confused and make everything harder than it actually is. Thank you for your service prof Dave!
I'm a 12 year old tryna learn calculus and also I'm from the philippines and glad to say,this helped me a lot!
+1 sub for you!
You can learn all high school, college math within a year by giving yourself a reason to do it for, since the brain is evolved to do certain tasks, for survival and reproduction. Save yourself a lot of time and money by doing AP exams way earlier, screw the norm brother.
Damn, respect to you. I'd never be able to understand this at 12.
@@bologna3464 facts lol
saan ka nagaaral?
You're wasting your childhood
Dude my AP calc exam is tomorrow and no one could explain substitution to me until you, I’m in debt and at your service!
Thanks a lot!!! I usually have no problem in maths but for some reason I simply wasn't able to wrap my head around integration by substitution. This really cleared things for me and lifted a huge burden!!
You're an amazing teacher! Pls keep up with the great work!
Dave - all I have to say is THANK YOU SO MUCH. This video was extremely helpful in developing my understanding of the substitution rule
Man you're genius. Every problem just make sense.
I stan this man and will forever thank him for existing i can already feel my calculus 2 grade rising
This actually helped me a lot! Thanks!
ua-cam.com/video/SbP3_d15yFc/v-deo.html
Professor Dave is my gratest teacher ever I have seen.I love your teaching methods
God bless you professor Dave, you are saving lives out here, emotional lives that is
Dear Dr. Dave, I would hereby like to submit a humble request for your consideration of the production of an additional calculus video, U-Substitution of Definite Integrals. There's some extra thinking involved, and I would love to see your 5-10 minute take on it. Thanks for all the amazingly helpful content!
Another best teacher across the world is our respected sir dave. Sir i am from india and still my all my country mates watch ur chnnl to ace science.
Your way of explanation made things pretty much easier
Do you have any advice for me learning calculus like in the video? I’m in high school and not doing too well :( . It’s hard for me as I have to juggle many subjects.
Just start at the beginning of the calculus playlist and work your way through?
ua-cam.com/video/SbP3_d15yFc/v-deo.html
I FINALLY GET IT!!!! I have a test tomorrow morning and substitution was the only thing I couldn't grasp. That passing grade's in the pocket for sure
Thank you so much Dave!!! I got a 100%!!
The best teacher on UA-cam.
Thank you professor
I needed someone to explain this to me like I was a child.
Thanks prof. Dave
You saved my life.Thanks that you are born.
Thank you sir for your dedication and for making this free! 🙏
What is the video in this series that is where Dave justifies the splitting of dx from d/dx to be able to "multiply" the integrand by dx to get 2x dx = du?
I finally understand my lesson in calculus. Thank you!
thanks Dave. I am preparing for my final exam for one of the hardest math courses!!! tnx
I'm sorry, I know this is said often but... holy cow. This man is up here explaining things that, a year ago, I would have understood about as well as Einstein's Field equations and yet I'm understanding it. The crazy thing is that even though it still sounds nerdy af (which is something I always used to appreciate, but wasn't really able to properly replicate due to a lack of understanding), it's not just going in one ear and out the other.
Now I'm not gonna say that it's solely Dave or even just solely UA-cam, but between last year and this year I went from failing at properly comprehending Pre-calc class to sucking in information on Calculus and planning on taking an exam to skip taking the first class all together, and I feel like it wouldn't be possible at *_nearly_* the speed it happened without UA-cam and Dave more than many. I could even say even Khan Academy hasn't helped as much.
Thank you, Professor Dave. I first came here for anti-conspiracy content... but I subbed for this.
2:02 this is what i needed to know, the teacher i was watching was explaining it so weirdly.
math with this guy is on another level
Thanks a lot!
Thank you Prof Dave!
THANK YOU THANK YOU THANK YOU‼️‼️‼️‼️ i cant believe that all of my questions abt the substitution rule have been answered with a short, 10 minute video!!! THANK YOU‼️‼️‼️
gotta love professor Dave, finally understood the concept after a WEEK of working on this!! gotta love him :D
Love From INDIA❤🇮🇳‼️
Thank you sir for this simple and best explanation on this topic.❤
Sir you don't even know how much of a headache and heartache you saved me from ❤️ 😭
Thank you Professor Dave
simple and easy steps to understand thanks Man
谢谢！
Hey so is it possible if you have an extremely long polynomial, that you can use the Subsitution method in two places in the polynomial at once? So if you had like two sets of parenthesis in a long poloynomial, could you substitute one for U and another for Y (random variable), and then do this method for these two different substitutions at the same time?
I watched third time and I took notes.
Thanks! I came for help with organic chemistry and stayed for the calculus help.
Thanks a lot sir, after long time of learning I've understood by yuor explanation
finally a video that explains this well.
Jesus you look like dave
Thank you prof. dave!
I'm totally using that smiley face variable on my next exam
thank you sir
Thanks a lot
Unajua mwanangu // awesome 👌
Thanks sir!
8:27 Shouldn't the minus sign become plus for the left part of equation, if we add it to both sides?
Thankyou❤️
Thank U, Prof. Dave.
9:43 The answers are in order: ln|x^2+3x| + C and -cos(ln x).
why is there a minus beside the cos?
@@ak_oneoneoneBecause the derivative of cos is negative sin.
@@MarioManiac81 ohh yah that makessenss
professor dave explains is so cool
I needed this like 3 years ago
It's not too late to learn now
Thank you!
It helped me
Thanks a lot professor ❤❤ love from Bangladesh
Professor Dave, please can you start a series on DIFFERENTIAL EQUATIONS?? Pleeeeaasseee??
2:15 where did you justified ehy its possible??????????????????????
Thank you Math Jesus
thank you
an amazing explanation brother
This guy is genuinely better than organic chemistry tutor. Things are always so clear and straight to the point.
I won’t stand for this Julio slander
truee both are good@@bonelessbooks9263
You are very wicked, organic chemistry tries his best,but you can't appreciate him
Thanks very much.
Thank you best professor 🥰
Thanks a lot brother
Hello, professor. I am just confused about the true answer in the integral of tan(x), if it must be ln |sec x|+c or -ln |cos x|+c? Thank u.
right?
Is the point in the substitution rule to simplify the equation? Cause if so i dont really see it it just makes everything more complicated than it already was. Either way, great video 👍👍
ua-cam.com/video/SbP3_d15yFc/v-deo.html
Thank you😊👍
Great Video! Solving integrals is allways fun!
You are doing a great job...keep it up
you are intelligent thank youuuuu
Thanks very much Prof. Dave!
For helping me to understand it more.
Thanks a bunch 💐🙏
For the second example that was shown, after applying u-substitution for it to then become du/3=x^2dx; what would happen to the x^2?
It (and dx) will be represented by 1/3 du. It's already part of it.
Thanks
Thank you sir! :)
U should say that x ≠π/2
Bcz if x=π/2
Than cos π/2=0
ln0= unlimited form
He teachers so cool man thanks!!
Calculus is life
I love you professor Dave
In which video does Dave tackle u substitution of definite integrals and how to change the limits of integration?
If it's my choice, I leave the limits of integration alone when doing u-substitution, and translate it back to the original variable of integration, before applying limits. Some integrals are not possible to do in closed-form as indefinite integrals, so that is the rare times when I opt to translate the limits to the u-world. For instance, the Gaussian integral.
2:15 anyone found that explanation later in this series? Which video should I be looking for?
unfortunately i haven't been able to cover that yet, i'm looking for someone to help me write differential equations content right now.
@@ProfessorDaveExplains what kind of help do you need?
I need someone to write the content, since I never went that far in math myself, I tapped out after linear algebra. If you think you're up for it shoot me an email!
Thanks sir
It helped a lot
Great!
Thank you so much 🥰 that was very helpful 😊
Professor dave, I have a question, is the U substitution the same as algebraic substituion?
It's called "U-substitution", because it is common to use U as the temporary variable for it. I prefer to use W instead of U, when both integration by parts and U-substitution are part of the same problem. It is not the same thing as algebraic substitution, but the term substitution means the same thing in both of these terms.
Ultimately what it means, is if you can recognize an integrand that is likely the result of a differentiation through the chain rule, then you can switch the variable of integration, to a variable that represents the inside of a function. Suppose your integrand is a product of g'(x), and the composition of functions f(g(x)). The g'(x) term might not strictly be the derivative of g(x), but rather you might have to multiply by a constant to get g'(x). In that case, you multiply by 1 in a fancy way, as a constant divided by itself. Part of that ratio becomes the constant you need in order to complete g'(x) to be, and the other part of that ratio, becomes a leading constant of the entire integral, that you pull out in front.
@@carultch Didn't even give you a thank you. What an asshole they are.
Understood very well, but in exams when I see the questions, I will forget all of it 😢😫
shoutout sa mga pinoy dito HAHAAHA thank you sir dave!
In which video of the series was it explained why we can manipulate differentials here? Thanks
Very amazing technique that can be shared to my classmates 🤗
how do you spend your day ?
I'm spending my days this summer self studying in advance for the nxt school year
thank you for the excellent explanation !!
i'd like to ask, with respect to the first trig example : "sin^6xcosx" why did you choose sin instead of cos, and in an exam how would i know which one to choose ?
if you choose cosx, then the integration proceeds as follows:
∫ sin^6(x)cosx dx
u = cosx, du = -sinx dx -> dx = du / -sinx
substitute u and du:
∫ (sin^6(x) u du) / -sinx
= - ∫ sin^5(x) u du
you can see here that x is still involved in the integrand even after u substitution, so this doesn't really accomplish anything.
generally when picking u values for trig functions, you want to pick the function whose derivative is in the integrand and will disappear after u substitution. this is so that the resulting integral will be nice and clean and convenient to evaluate
you are a star
I watched a 30 min long video on yt... Not gonna take his name... And I was completely lost
I couldn't understand a shit
And then i stumbled upon ur video... Seriously everything is easy now... A bad teacher can make u feel dumb.. really
Thanks dude for telling me the correct path when I got lost with that random youtuber
I always go back to this video whenever I can't remember how to do u substitution. It's been almost a year already