Integration Using The Substitution Rule
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- Опубликовано: 6 май 2018
- With the basics of integration down, it's now time to learn about more complicated integration techniques! We need special techniques because integration is not as straightforward an algorithm as differentiation. The first technique we will add to our bag of tricks is the substitution rule. Check it out!
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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.
Dave - all I have to say is THANK YOU SO MUCH. This video was extremely helpful in developing my understanding of the substitution rule
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!!
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!
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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.
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gotta love professor Dave, finally understood the concept after a WEEK of working on this!! gotta love him :D
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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 RUclips, 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 RUclips and Dave more than many. I could even say even Khan Academy hasn't helped as much.
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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!
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‼️‼️‼️
God bless you professor Dave, you are saving lives out here, emotional lives that is
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.
This actually helped me a lot! Thanks!
ruclips.net/video/SbP3_d15yFc/видео.html
Your way of explanation made things pretty much easier
Thanks very much Prof. Dave!
For helping me to understand it more.
Giga god, i thought d/dx was just the notation as well. Thanks for not skipping over that explanation like others.
Thanks prof. Dave
Thank you Prof Dave!
Thanks a lot sir, after long time of learning I've understood by yuor explanation
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?
simple and easy steps to understand thanks Man
I finally understand my lesson in calculus. Thank you!
Thanks a lot!
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?
The best teacher on RUclips.
You are doing a great job...keep it up
Thank you professor
Sir you don't even know how much of a headache and heartache you saved me from ❤️ 😭
Thank you so much 🥰 that was very helpful 😊
Thank U, Prof. Dave.
Great Video! Solving integrals is allways fun!
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In which video of the series was it explained why we can manipulate differentials here? Thanks
finally a video that explains this well.
an amazing explanation brother
Thanks sir!
second number in evaluate, why did the f turn to F(x) and in turn getting a negative sign beside the final answer? appreciate the help
professor dave explains is so cool
Thank you best professor 🥰
Thankyou❤️
Thanks! I came for help with organic chemistry and stayed for the calculus help.
Professor Dave, please can you start a series on DIFFERENTIAL EQUATIONS?? Pleeeeaasseee??
thank you sir
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%!!
8:27 Shouldn't the minus sign become plus for the left part of equation, if we add it to both sides?
I needed someone to explain this to me like I was a child.
Thanks a lot
Thanks very much.
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?
ruclips.net/video/SbP3_d15yFc/видео.html
thank you so much!
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This was very helpful, but around 6 :39 when you bring the 3/2 to the front why does it become 2/3 ?. Is there a rule that i don't know about? Lol..I mean if it was say 4 then we bring it up to the front and make it 1/4 , so why on this case do we flip it? Thanks@!
Thanks a lot brother
thank you
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.
Jesus you look like dave
2:15 where did you justified ehy its possible??????????????????????
Thanks a bunch 💐🙏
It helped me
Thank you sir! :)
U should say that x ≠π/2
Bcz if x=π/2
Than cos π/2=0
ln0= unlimited form
I needed this like 3 years ago
It's not too late to learn now
What is the video where he explains why algebraic manipulation is possible?
you are intelligent thank youuuuu
Thank you😊👍
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
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?
I love you professor Dave
how to know where to use substitution method
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 👍👍
ruclips.net/video/SbP3_d15yFc/видео.html
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.
Thanks
Calculus is life
Thanks sir
It helped a lot
Great!
Thanks! It was a good explanation, but now how do we change the intervals according to u?
I prefer to leave the limits of integration alone, and translate the result of integration back to an indefinite integral in the world of the original variable of integration. But if you prefer, you can recall how u is a function of the original variable, plug in your limits to calculate corresponding values of u, and then make those corresponding values of u, your new limits of the integral.
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What have I been doing in high school? I didn't learn anything back then. Now, I understand everything. Where were you Professor Dave when I needed you?
Unajua mwanangu // awesome 👌
Thank u very much may Allah blessed you with happiness I don't I have words to thank u one day before exam very helpful video 😊💞💜💞💜
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.
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Thanks professor, now calculus seems reasonable, greetings from Mexico
I'm totally using that smiley face variable on my next exam
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.
@@user-hu4jd7hr4f ohh yah that makessenss
Very amazing technique that can be shared to my classmates 🤗
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I'm spending my days this summer self studying in advance for the nxt school year
soo helpful,,, thank you sir
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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
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