Dr Peyam, it's incredible how your work from a very distant place from my place (Brazil) can do so much for students like me from here. I really need to thank you.
I spent an hour struggling with these questions and then I found your video. 😭😭😭 I'm so glad I did. Now I have 0 problem solving these types of question.
Question how does this help say in evaluation the integral from 0 to 1 when i did it with a computer i got different results as opposed to(1-cos(1)) * 0.5. Also i did sin(x²+y²) and parametrized to get sin(r²) * r dr dΘ and got the same result but had to divide by 2π. Is this a valid approach.
Awesome integral! While I still can't do double integrals like that I'm glad this time I could atleast understand it, a simple but elegant solution. Hey Dr. Peyam, what do you think about michael atiyah's supposed proof of the rieman hypothesis? I haven't watched his whole video on it, and I really want it to be true, but I've seen some skepticism of it on the internet
Haha, I’m torn because I don’t think it’s something that’ll be proven in our lifetime, but on the other hand Michael Atiyah is a really smart and famous mathematician! Let’s see what the math community says; don’t trust the internet anyway!
I have no clue what the Todd function is, and couldn't find any info on it. How "obscure" was it? How did he pulled that off? The proof he presented doesn't really convince me aswell, however, if it turns out it IS, it is a turnover in history, a BIG history in turnover. I hope that I can study his proof in the future more in-depth. However, I think the best is to wait a bit for the time being.
I also proved that the Lebeasgue measure, cardinality, ect. of the set of differentiable almost everywhere functions is the same as that of the set of real numbers.
@@drpeyam Ohh okay cool! So we pretty much always work it out first and if it's impossible we erase all our work and then change the order and start again? (I hope that makes sense!)
actually it is posisble without fubini's thoerem because you can just do this ∫_0^1∫_x^1sin(y^2)dydx, let f(x) be an anti derivitive of sin(x^2) with respect to x with the constant set to 0 ∫_0^1∫_x^1sin(y^2)dydx=∫_0^1f(1)-f(x)dx=f(1)-∫_0^1f(x)dx ∫_0^1f(x)dx=xf(x)]_0^1-∫_0^1 x*f'(x)dx=f(1)-0f(0)-∫_0^1 x*f'(x)dx=f(1)-∫_0^1 x*sin(x^2)dx f(1)-∫_0^1 x*sin(x^2)dx=f(1)-1/2*∫_0^1 2x*sin(x^2)dx=f(1)-1/2*∫_0^1 sin(u)du=f(1)-1/2*(-cos(u)]_0^1) =f(1)-1/2*(-cos(1)-(-cos(0))=f(1)-1/2(1-cos(1)) D(-cos(x^2)/2)=-(-sin(x^2)/2)*(2x)=xsin(x^2) -cos(1^2)/2--cos(0^2)/2=(1-cos(1))/2 =f(1)-∫_0^1 x*sin(x^2)dx==f(1)-(f(1)-1/2(1-cos(1)))=f(1)-f(1)+1/2(1-cos(1))=1/2*(1-cos(1)
I cry all night when Dr Peyam doesn't upload lol (that was a funny joke Dr Peyam; I hope people don't cry over integrals (especially unsolvable ones either) )
Hey there! I love your channel and I came here to ask you for help. Could you solve the definite integral of (x-1)^n/sqrt(1-x^2) between 0 and 1 where n is a positive integer ? Thank you very much for your videos !
Looks like Dr Peyam had a tea with papa Fubinni
Indeed! It was delicious, but he kept changing the order of the flavors 😂
Dr. Peyam's Show LoL
This needs to be posted
I can already hear people cracking
FUBINI
There's just something about his vibe , like , WOW ! You genuinely deserve the best in life . Does anyone else see this ?
Dr Peyam, it's incredible how your work from a very distant place from my place (Brazil) can do so much for students like me from here. I really need to thank you.
1:53 THAT is an extremly nice and intuitive way for describing the region....
I spent an hour struggling with these questions and then I found your video. 😭😭😭 I'm so glad I did.
Now I have 0 problem solving these types of question.
your smile is very contagious. thanks for the vid
Kfc hates when you change your order but i see you have no fear lol
Love the video
😂😂😂
8:27 A Math quickie is my favorite type of quickie
Fubini's theorem is the most useful theorem out there
Loved your passion for teaching 😎😎
5:50 ahhhh so that's the whole reason you change the order of integration. Thank you
I like your videos and your humour sense!
thanks man, straight to the point and well explained
Thank you!!!
amazing explanation sir........... love from India
Hi, love your videos
I’ll try :) There are some other ones on my channel
Teachers like him actually exist
I take that as a compliment :)
if you could just see the teachers here in India......
you would know why I like you so much
Thank you for your thorough explanation! helped me a lot!
Question how does this help say in evaluation the integral from 0 to 1 when i did it with a computer i got different results as opposed to(1-cos(1)) * 0.5. Also i did sin(x²+y²) and parametrized to get sin(r²) * r dr dΘ and got the same result but had to divide by 2π. Is this a valid approach.
Your classes are just assume 👌🏻👌🏻👌🏻👌🏻👌🏻. I love to learn from you and become a greatest fan of your classes.
thank you for helping me prepare for integration exam
Thank you. Your videos are really helpful for us... Colegio de Postgraduados, Chapingo, Edo. de México.
Great, thanks a lot Dr. Peyam. (outside has to be a constant. thank you)
Awesome integral! While I still can't do double integrals like that I'm glad this time I could atleast understand it, a simple but elegant solution. Hey Dr. Peyam, what do you think about michael atiyah's supposed proof of the rieman hypothesis? I haven't watched his whole video on it, and I really want it to be true, but I've seen some skepticism of it on the internet
Haha, I’m torn because I don’t think it’s something that’ll be proven in our lifetime, but on the other hand Michael Atiyah is a really smart and famous mathematician! Let’s see what the math community says; don’t trust the internet anyway!
I have no clue what the Todd function is, and couldn't find any info on it. How "obscure" was it? How did he pulled that off? The proof he presented doesn't really convince me aswell, however, if it turns out it IS, it is a turnover in history, a BIG history in turnover. I hope that I can study his proof in the future more in-depth. However, I think the best is to wait a bit for the time being.
I also proved that the Lebeasgue measure, cardinality, ect. of the set of differentiable almost everywhere functions is the same as that of the set of real numbers.
Hi dr peyam. Do more videos on real analysis plz because I love it!!!!!!
More videos to come! And there’s a whole playlist if you’re interested
OMG DR Peyam,They just dropped the restriction on your class,I enrolled :).
YAAAAAAAAAAAY!!!! See you on Friday 🙂🙂🙂
omg thanks for this incredible explanation it helped me a lot
But how you indentify yourself?
thanks a lot from belgium!
Hey Dr Peyam, I was wondering if you can please tell me how do I know when to change the order of integration? It's not making any sense to me.
If the function is impossible to integrate
@@drpeyam Ohh okay cool! So we pretty much always work it out first and if it's impossible we erase all our work and then change the order and start again? (I hope that makes sense!)
Yep
@@drpeyam Awesome! Thank you so much for your time Dr Peyam :)
if the region is under the x axis, will it become positive?or negative?
I love your energy
Does make sense an integral of a diferential in the argument of a function? Ex: integral of sin(dθ)
It’s more of a notation in measure theory and probability: If m is a measure, then m(dx) means integral with respect to dm
Dr. Peyam's Show wow cool, thanks! i even thought it wasnt something yet, hahaha
2:34, you cheated us. You said "lets add some fun" but you added a bar.
I love your energy, sir. thanks so much for the explanation!
smooth going and very clever!
is the integral impossible without Fubini's theorem? or is the integral, sin(y^2), impossible with respect to y?
Yeah, it’s one of those functions with no (elementary) antiderivatives
ah I see, thank you!
actually it is posisble without fubini's thoerem because you can just do this
∫_0^1∫_x^1sin(y^2)dydx,
let f(x) be an anti derivitive of sin(x^2) with respect to x with the constant set to 0
∫_0^1∫_x^1sin(y^2)dydx=∫_0^1f(1)-f(x)dx=f(1)-∫_0^1f(x)dx
∫_0^1f(x)dx=xf(x)]_0^1-∫_0^1 x*f'(x)dx=f(1)-0f(0)-∫_0^1 x*f'(x)dx=f(1)-∫_0^1 x*sin(x^2)dx
f(1)-∫_0^1 x*sin(x^2)dx=f(1)-1/2*∫_0^1 2x*sin(x^2)dx=f(1)-1/2*∫_0^1 sin(u)du=f(1)-1/2*(-cos(u)]_0^1)
=f(1)-1/2*(-cos(1)-(-cos(0))=f(1)-1/2(1-cos(1))
D(-cos(x^2)/2)=-(-sin(x^2)/2)*(2x)=xsin(x^2)
-cos(1^2)/2--cos(0^2)/2=(1-cos(1))/2
=f(1)-∫_0^1 x*sin(x^2)dx==f(1)-(f(1)-1/2(1-cos(1)))=f(1)-f(1)+1/2(1-cos(1))=1/2*(1-cos(1)
Thank you Dr. Peyam, this helped a lot for my take home calculus exam! You're the man.
Amazing, congrats!!
This was so helpful thank you!!
I cry all night when Dr Peyam doesn't upload lol
(that was a funny joke Dr Peyam; I hope people don't cry over integrals (especially unsolvable ones either) )
LMAO 😂😂😂
sir integration of sin is equal to - cos right .....?then why r u right integration of sin is equal to sin ?i'm confused🧐🤔🤔
Hey there! I love your channel and I came here to ask you for help. Could you solve the definite integral of (x-1)^n/sqrt(1-x^2) between 0 and 1 where n is a positive integer ? Thank you very much for your videos !
nice one! thank you!
btw I
Thanks ❤️
THANK YOU
COMPLEX DOUBLE INTEGRAL AND SWITCHING OF x AND y!! :3
Awwww shit! It's getting real!
Thank you
thanks!!
no more one direction with multivariable calculus? thank god, no more one direction :P
Cool
im male lol
thank you