Leibniz' rule: Integration via differentiation under integral sign

[@wmd44110]

I dealt with this in calculus, and now Leibniz has come back to find me in philosophy class. This guy was EVERYWERE!

[@DrChrisTisdell]

I'm glad you liked this one! The general "Leibniz method" is very useful for evaluating extremely challenging integrals (much more difficult integrals than the one in this video),

[@darkconjure]

Saves a lot of grief for some one reviewing this rule. Thx

[@TheLeeMrLee]

thanks for this video- I'm an A-level student in England, going to uni for maths starting this september, and I've been trying to read around some more advanced material from the standard A-level syllabus and I came across this method of integration, and despite my best efforts, I could not understand it until I saw this, thanks a lot :D

[@DrChrisTisdell]

Hi jslashs, I've been on holidays this week, but will try to post something tomorrow night so you have the weekend to look it over before the test.

[@REFG89]

I agree with jslashs - leibniz's rule seems to be one of the more difficult concepts in the course and there are not enough examples in the lectures notes/course pack to be able to understand the variety of leibniz questions in the tutorial problems - some more videos would be great :) Cheers

[@DrChrisTisdell]

Hi REFG89, I've been on holidays this week, but will try to post something tomorrow night so you have the weekend to look it over before the test. Make sure you study the sample tests that I posted on My eLearning Vista!

[@frelsmeg]

Dr Tisdell, What about the case when the integration variable and differentiation variable are the same ? For example, how would Leibniz's rule be applied for evaluating: dx_dt of the definite integral ?

[@fcmitroi]

@DrChrisTisdell I teach and I am a PhD student in mathematics.Your videos are very interesting to me (I discovered them just few days ago), not only from math viewpoint, but also the style of your talks and the fluency of ideas and language. Math history is quite interesting but there are too many Bernoulli there, we should count them like French people count their Louis (1st, 2nd, 3rd). I saw Norman's name in your subscriptions list, so I intended to look at some of his videos. Thank you.

[@DrChrisTisdell]

theneltrajan: you're right, I don't use "voice modulation' in these clips like I do in class. However, if you check the latest "Lagrange multipliers" vid then at 0.52 and 2.00 there's just a hint of an accent!? :-)

[@himmatpanag]

Hey, do these videos cover all or more of the UNSW course Higher Several Variable Calculus MATH2111?

[@jediwhelan]

Hi - great video, and i understand Leibniz's rule. But can you help me with the substitution you refer to at the start please. I understand if you make the substitution x = a * tan(t) then dx = a sec^2(t) dt and after using the identity tan^2(t) + 1 = sec^2(t) INT 1/a dt right? but how do i deal with the limits? Or have i gone about the substitution wrong. Many thanks for the help, i just lost an hour of my life!

[@DrChrisTisdell]

Great question Jedi! The new limits will be $0$ and $\pi/2$. Can you see why? (Hint: draw the graph of $tan x$ to gain some insight). Good luck!

[@SolidSnyder]

Thanks so much! I've been working on the first derivative of the gamma function today, and that helps a lot.

[@DrChrisTisdell]

@mangymetal I believe that both variations are OK - I have seen both spellings of each name, however, Wiki uses the spelling "Leibniz". My understanding is that both my versions of L'Hop/L'Hosp are correct. Best wishes .

[@DrChrisTisdell]

Hi REFG89 - I've posted another vid on this just for you and jslash!

[@DrChrisTisdell]

@fcmitroi : ) The older I get, the more interested I become on math history. Do you know Norman Wildberger ( his channel is njwildberger )? He has an excellent playlist on the history of math. You obviously have a very good knowledge of mathematics - are you a mathematician / teacher / researcher?

[@DrChrisTisdell]

@fcmitroi This is a question that I pose each year in lectures to my students. It is an interesting story about his association with Bernoulli.

[@nagarjuna84]

Doubt, 4:13, -2a is a variable, how would you move it to the other side. Please explain

[@atobias95]

Nagarjuna battula Since he is integrating with respect to x, he can treat alpha as a constant; thus, it does not matter whether it lies on the inside or outside of the integrand

[@nagarjuna84]

No, x is a constant there. He clearly wrote I'(a) there. He also wrote do/do(a) in the next step. So alpha must be the variable and i didn't see anyone moving variable out side the integrand. Integral x/1+x^2 not equal to integral 1/1+x^2. I have come like that.

[@MrG0CE]

WHAT'S INSIDE THE INTEGRAL IS RESPECT TO X, NOT TO ALPHA ! THAT'S WHY HE COULD TAKE THAT CONSTANT OUT OF THE INTEGRAL ! GO AND CHECK THE FUNDAMENTAL THEOREM OF CALCULUS, YOU'RE CONFUSING THE VARIABLE ALPHA OF THE FUNTION I WITH THE VARIABLE X OF THE INTEGRAL, THEY'RE 2 DIFFERENT THINGS !

[@DrChrisTisdell]

Thanks for watching! Around the 25 second mark I mention how to evaluate the first integral (so that you can verify the expression for $I$ is correct). Good luck!

[@DrChrisTisdell]

Always great to get your feedback! :-)

[@fcmitroi]

So, maybe you should have a video about the history of mathematics. You are a very good storyteller too, I am sure.

[@DrChrisTisdell]

@mangymetal L'Hopital or L'Hospital? :-)

[@fcmitroi]

@DrChrisTisdell L'Hospital was French (Guillaume François Antoine, Marquis de l'Hôpital ), so the French version of the name is L'Hôpital since they use the word hôpital (means hospital). So, you should write L'Hôpital. I know, the books are full of L'Hospital... Better write Bernoulli, it is easier and everyone knows how to write it. Problem solved. :)

[@fcmitroi]

@DrChrisTisdell So, maybe you should have a video about the history of mathematics. You are a very good storyteller too, I am sure.

[@DrChrisTisdell]

Thanks for the feedback!

[@DrChrisTisdell]

@fcmitroi :-) The older I get, the more interested I become on math history. Do you know Norman Wildberger (username njwildberger )? He has an excellent playlist on the history of math. You obviously have a very good knowledge of mathematics - are you a mathematician / teacher / researcher?

[@DrChrisTisdell]

Hi jslash - I've posted another vid on this just for you and REFG89!

[@urdream8]

please I need an urgent help did any one know how to integrate EXP[ x^4 + x ]  I need it in my programm pleaaaaaaaaaaaassssssssssse help

[@mangymetal]

Leibniz or Leibnitz?

[@jackleong4489]

It's really helpful :) and it's my tutorial question as well :) just had my exam today :)

[@DrChrisTisdell]

No worries!

[@beinanye]

Thank you! it is really useful and easy to understand!

[@rohanism26]

Nicely done sir....

[@DrChrisTisdell]

Thanks Malangsufi!

[@Malangsufi]

ur the best sir:D I really really needed this. tx

[@DrChrisTisdell]

You're welcome!

[@shubhamkhorvi1561]

Nicely done sir.. ty 4 making da video

[@DrChrisTisdell]

Hey, you're welcome!

[@DrChrisTisdell]

Great!

[@yasiryazdaniy]

Thank you sir from India

[@mganrock]

You are the Best!! Thank you very much..

[@mid01z]

i knew that "alpha" is a constant.. so how i deffrentiate a function by constant !!!!

[@DrChrisTisdell]

Treat alpha as a variable. After you have differentiated, then replace alpha with the particular value you are interested in.

[@mid01z]

Dr Chris Tisdell Dr chris ..thnxx for your response ...ia hve a question if treated alpha as a varible from the begging then I cant even integrate that equation from the begging bec I integrate due to x then what I will do about the variable alpha and if I integrated due to x and treated alpha as a constant ...then I will have an arbitrary constant at the end that is functin of alpha sooo I stiill dont have the the exact solution

[@mid01z]

Dr Chris Tisdell Its a weird thing sometimes I treat alpha as a constant and some times not !!!!

[@popopopoppy]

Thanks a lot! Really helps!

[@KellyPedro]

Thanks.

[@mangymetal]

@DrChrisTisdell L'Hopital .. i guess xD

[@emmanuelfriggieri]

you're amazing

[@simurgsoakinshield6101]

ben niye anlmıom mkcam ya gene kaldık iyimi...

[@DrChrisTisdell]

You're welcome!