how to integrate using u substitution
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- Опубликовано: 20 авг 2016
- Understand u-substitution, essential examples,
integral of sec(2x)tan(2x), @0:30
integral of sec^2x*tan^2x, @3:57
integral of sin(x)/(1+cos(x)), @8:07
integral of sin(x)/(1+cos^2x), @16:53
integral of x*sqrt(x^2-1), @23:22
integral of x*sqrt(x-1), @27:00
You make calculus a lot easier :')
Thanks
Glad I found this channel , awesome
15:29 You could get rid of that minus sign by swapping the limits of integration.
This reverses the area into its negative, which would then cancel with the minus sign ;)
That would lead to less noise with the minus signs afterwards ;J
21:15 Same here.
This is by far the best explanation outside of visiting my professor during office hours that I’ve ever seen apropos this topic. Thank you for this wonderful video!
Really helpful. Thank you & keep up the good work!
You are very enthusiastic and helpful. Thank you for making this easier to many students worldwide.
Thaaaank you your method really makes sense to me, when I learned at the classroom I was confused but now I can solve
5:15
sec(x) is not a good choice for you
Okay, noted, thank you for reminding me because i might choose sec(x) soon in my life
thank you so much for your amazing teaching style...it really helped me understand it in a much better way . also now I am able to solve questions much much faster .you are awesome sir
Magnificent video! Thanks for a great explanation
Thank you so much for this! You make it so easier and funny, greattings from México :D
You are an amazing teacher. Thank you so much
Loved your videos, great channel ! Congratulations
Thank you~!
dude you just saved me a quiz grade thank you so much
this is the best channel on youtube!
So goated. I have my AP Calc exam in 2 days and I forgot all this but now I'm good to go. Thank you.
it`s amazing! Thank you!
WOW! You make calculus a lot easier :')
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i didn't even realize
dripping subtly
thank you very much
Such an amazing video
Omggg thank youuuuuuuu so muchc
man i wish you were my calc teacher (i love my current calc teacher but you're also amazing)
love u bro. this was very helpful.
Glad it helped
10:50 The first integrand is just `tan(x/2)` though (remember the half-angle formulae for tangents?).
So maybe this fact can be used here somehow?
Also, I find it kinda interesting that integrating the tangent on a quarter-circle can give us `ln(2)` :>
Never heard of sec(x) before this channel.
Good dear.........good...Exellent...arrangement...for....explaination ..
i love the way he teach tbh
This man is a legend
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Please when you have x^n/2 with n/2 > 1, divide the expression in terms of x^(positive interger) times x^(1/2)
Thank you
For the one at 3:57 Couldn't you pick u=secxtanx (becomes integral u^2)
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16:40 dount u need to go back to DX function? putting 1+cosX in the Ln(u)?
I think I have single-handedly learned calc1+ lv math just by watching your videos.
PS: My class just started with derivative.
3 years ago :O
@@kepler4192 yep, I'm at my second year of physics major, time really flies.
@@wenhanzhou5826 indeed, I’m at 3rd year highschool, these videos have made me better at calculus and now I’m the only one with a full mark in my entire class in calculus
@@kepler4192 great to hear, these videos are really helpful and I believe you will go long with it 😊
@@wenhanzhou5826 definitely! 👍
This is great Sir ...best I have seen in years. I noticed you stay in the "U world" when you evaluate these integrals. What happens if you go back and place the original substitutions back and calculate the integrals with the original boundaries?
Then u would get same answer
You could have also used DI method for 30:19, right..?
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The last question is osm....
LUL, I just wanted to recap IBP for doing old exams and the integral for which I looked this up is exactly the first one ((sin x)/(1 + cos x)) from 0 to pi/2 :D
Substitution u=1+cos^2(x)
will work if he has integral Int(sin(2x)/(1+cos^2(x)),x=0..π/2)
How did arctan come about in 22:24
1. Is there a method to know what substitution will work without having to go through trial-and-error? Because, you know, it takes time, most of which is wasted if you make the wrong choice :P (and time is money, not only on tests).
2. Sometimes substitution won't work no matter what you choose. How can we know this beforehand to avoid beating the dead tree?
This technique seems to work only for functions which are multiplied by the derivative of the internal function.
This is kind of like a kid learning long division asking if there's any way to know when you're doing 75/13 whether to start with 4 or 5 or 6 without trial and error. Well, yes, there is, but the trick is to be good at multiplication. While learning those skills, there's no real trick other than trial and error and then over time and with pattern recognition and better multiplication skills, he'll just be able to see it.
The same is kind of true here. The method to know what substitution will work out to let us cancel the terms we need to. So, similar to the trick to being good at division is being good at multiplication, the trick to being good at integration is to be good at derivatives. Until then, though, trial and error it is :)
So the moral is, basically, that even if two integrals look almost the same, the technique used to solve each of them is usually completely different? :P That doesn't sound very comforting... :q
🙏🙏🙏
Hi, i tried to solve integral of sin(x)dx/(1+cos(x)) from 0 to pi/2, when i let u = -cos(x) => du = sin(x) dx, lower bound = -cos(0) = -1, upper bound = -cos(pi/2) = 0, int of du/(1 - u) from -1 to 0 = ln|1-u| from -1 to 0 = ln|1| - ln|2| = - ln(2)
I cant find where i have made a mistake( i'm sure that there should be only positive value , because sin(x)/(1+cos(x)) is non-negative on [0;pi/2]). What is wrong?
lol , sorry, i forgot to multiply whole thing by (-1). My bad
Sir make a playlist about definite topics, it will help us a lot sir ! ie. if you make a video which contains differentiation and integration then just put the video on the playlists "Differentiation" & "Integration" . I think its a nice idea and people will love it.
I have a website: www.blackepnredpen.com and you can go to calc 1 or calc 2 for it.
@@blackpenredpen thank you so much
@@blackpenredpen you type pretty fast ! it will be www.blackpenredpen.com
lol, yea, thanks!
@@blackpenredpen man i love your teachings ... :3 actually dont wanna share your teachings w anyone :3 hehe
PLEASE DO HARDER QUESTONS LIKE SIN^7 x cos^ 8 x etc
That's easy bruh come on..
I see a talent
What do you do if you pick a “U” and it’s derivative doesn’t completely cancel the other term?
Either find a different U or use a different method; for example, sometimes it’s necessary to integrate by parts. A quick and dirty summary of integration by parts is that it inverts the product rule similarly to how integration by substitution inverts the chain rule.
Why is the integral of -1/(1+u^2) equal to -tan-1(u) and Not cot-1(u) ??
It's both. -arctan(u) and arccot(u) only differ by an added constant.
+C.
4:00
•1/2.
(1)=sec(2x)
I have nice u substitution for you
integrating functions with roots
R(x,sqrt(ax^2+bx+c))
sqrt(ax^2+bx+c)=u-sqrt(a)x a>0
sqrt(ax^2+bx+c)=(x-x_1)u a
Actually.
So I lost you at the very start
Thats Why leave space. Eh?
The music is distracting.
I can show you the (u) worlddd
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