Integration by Parts

[@aloixasinclaire9911]

What would make this even better, is children in the background asking questions about the process while you're going through it! :) Or saying "I finally get it!!!"

[@hisoka7489]

children?

[@-Quasar-]

@@hisoka7489you’re weird asf dawg

[@MartinZimba-su4uf]

I regret coming to know about you so late ,,you are excellent professor ,, The way you teach is no much to many,,

[@guidoreuter6032]

Excellent!! Great idea to relate IBP with the Product Rule for differentiation. Thanks, from a retired 68 years young math enthusiast.

[@punditgi]

I love 💘 this channel! An awesome teacher. 😃👍

[@jan-willemreens9010]

...Good day Newton, I hope you're still going strong. For the integral of sin(x)cos(x)dx one could also use the well-known trigonometric identity of sin(2x)=2sin(x)cos(x) --> sin(x)cos(x)=0.5sin(2x), and thus solve the integral of 0.5sin(2x)dx instead. For me, this is what makes mathematics so much fun, namely to look for as many possible solution strategies; just like you always say at the end of a presentation, keep learning to stay alive! Thank you for another inspiring presentation... Take good care, Jan-W p.s. L I A T E, remember?

[@PrimeNewtons]

I remember LIATE. Just as I began reading your comment, I said to myself, this is actually cooler than my method. Like we both agree, I Never Stop Learning. Good to read from you again.

[@MariinaNuuyoma]

The biggest goat 🐐 on this app

[@nadwala_mumala64]

Here is me wondering if you're American or Nigerian 😂😂. Great vids sir. I am a new member just figured you out today. I'm sticking to you ❤😊

[@marymumba9760]

Thanks to you sir

[@christopherramsey6001]

Wonderful explanation ! Thank You !

[@IsaacPhalula]

Thanks for the wonderful explanation

[@henrygalvan9333]

Great work sir

[@holyshit922]

In integration by parts we have to choose parts u = f(x) and dv=g(x)dx We choose parts in such way that Integral of vdu is easier to calculate When integrating dv=g(x)dx we can put any constant we want and sometimes it will be better to use other constant than zero because this other constant may allow us to do some cancellations offtopic I will try to parametrize your t-shirt equation to easier calculate area enclosed by curve or length Length of this curve probably would not be expressed with finite number of elementary functions and operations like additions , multiplications Let x=cos(t) y-cos(t)^(2/3)=sin(t) So your curve should be x(t)=cos(t) y(t)=sin(t)+cos(t)^(2/3) t in [-pi,pi] Why programs like Wolfram draw only half of this curve although on interval (-pi..-pi/2) or (pi/2,pi) x(t) = cos(t) is negative (they draw only non negative values for x(t)) but parametrized equation may simplify integration Ok programs like Wolfam have problems with taking roots of negative numbers Parametrization i gave should be ok

[@PrimeNewtons]

That's quite insightful. I need to find that T-shirt too 😀

[@memotto123]

24:35 the train is calling “+ c”:)

[@jagsittermedsimonochjobbar]

King

[@fredo5923]

19:45 + c!!!

[@WarriorBane]

Nice shirt

[@printerprinter1225]

man, i wish u are my lecturer , hell mine is terrifying , the lesson is boring , his voice is so little that even though i am sitting the 1st row, i still barely heard his voice

[@HenryBriskin]

What is the order rule lLATE

[@aalekhjain2682]

Its usually LIATE and not ILATE. LIATE stands for Logs, Inv Trig functions, Algebraic func, Trig func, Exponentiation func. This is a trick to pick u for IBP. It is because its easier to differentiate and deal with du if u is a simpler function.

[@bruhnish598]

POV: you went to desmos to graph the function on his shirt

[@marymumba9760]

Thanks to you sir