Integration by substitution (visualised)

[@aleenavirdee5656]

Absolutely fantastic! 👏 You’ve got a special talent with which I’m sure you will help many many students understand maths concepts in ways they never would have before. With content like this there is no doubt about it that you will go very far!

[@Abdullah-kw6kk]

All of this for free; amazing and much appreciated

[@aaronnanoo1887]

I loved the penalties ending to the football analogy, a great way to explain the concept of integration by substitution!

[@okayokays9926]

Wow! Excellent animations! I have never seen integration by substitution visualised! Great work!!

[@vathanagopinath8466]

Love the clear animations and easy to follow explanations!! You made a seemingly difficult concept a lot easier to understand so it will definitely stay in my memory now!

[@DiLLZGFX]

The visuals are absolutely amazing and really helped me grasp the concept!

[@aromeran]

I saw the thumbnail of this video on 3B1B and I don't regret looking for it

[@BhavdeepSoor]

Very clear and concise and a brilliantly informative pace! 👏🙌

[@cynthiako94]

It's great to see maths explained in more creative ways, very engaging and informative!

[@ДмитрийСкрябиков-ж6э]

It's amazing! I'm glad to see FREE PDF file in your website. Your video also fantastic! I anderstood this theme immediately after watching your video! AMAZING!

[@Veptis]

Ask my professor today if there is a geometric interpretation. And they said there might be but that's not what they want to teach. And that really made my sad. I looked it up on KZbin and there were only a few videos that had visualizations. Thank you for providing what I was trying to figure out in my head alone. Would have loved to get the visualizations for the examples as well. And find how it's transformed to get the new borders in the substitution

[@douglasstrother6584]

That's a bummer: calculus is fundamentally geometrical, such as Cavalieri's Principle. Check out 3blue1brown as well.

[@rektlzz7808]

Even though the substitution method is pretty intuitive, it's good to see visually why it's true. Great job!

[@DamianWaynes]

This is by far the best explanation I've ever seen for u-sub. Please keep making more content

[@ejsafara456]

oh my god, this has helped me SO MUCH, the animation was ON POINT i now UNDERSTAND thank you for the video ^^

[@nikkibhamra7536]

Absolutely awesome really good explanation about integration by substitution 👏🏻👏🏻👍🏼

[@navneetkaur2445]

Thank you for this amazing video. It is very detailed and helpful. Also I love the animation!

[@iplgeek]

Beautifully made! This is a lovely angle to take, and also hints at the relationship to Jacobians in multi. Loved the visuals and explanations :)

[@indisingh2990]

Great explanation about integration love the visual.

[@punditgi]

Brilliant! Best explanation anywhere! 😃

[@Arycke]

6:02 , the indefinite integral should have had abs value around f(x), bc f(x)=x+1 has negative f(x) values. I.e. ln|(x+1)| + C, where x ≠-1 Original function had domain (-inf,-1)U(-1,+inf) You get an anti derivative at every point defined in the original domain.

[@Arycke]

Still an awesome visualization. Thanks for this, sir.

[@lukollolak6219]

How is to possible I haven't seen this video earlier. It would have helped me sooo much. Visualizing like this is uncomparable to solving definitions and proofs

[@Bedoroski]

Great work.

[@m.d.asgarmansuri5731]

Thank u so much for your fine work

[@skaur6838]

Brilliant explanation and animation Love it! Very clear, students will love the motivation in your voice 👍keep up the good work 😃😃

[@IlIlllIlll]

Thank you so much for this visualization

[@Dinesh123lol]

Amazing video, very clear explanation. Thank you!

[@vaaniakapooronbehalfofaliz2187]

Super informative! Love the visuals

[@janhavikulkarni9893]

This is was so well explained!!!

[@justadreamerforgood69]

You're a snack 🥨

[@zyggzag4154]

Thank-you! legend!

[@ShuyuLin-sh2gk]

Hi, it is fantastic！🎉 and where is the problem sheet？

[@sukhibhamra5750]

Fantastic explanation thank you so much 👏🏻👏🏻👏🏻

[@alifrahman7099]

Amazing!

[@AbdulAziz-fg2cy]

beautiful ANIAMTIONS

[@Elvisitante]

What graphing machine are you using at minute 2:46? please, please👏

[@nhatkhang7363]

2:28 why when x= 2 then y=3 and u=4 then y also equal to 3 ?

[@lindie5830]

I also found this to be a jump

[@josealejandroconstantinola7520]

Sir what application ypu used in this presentation?

[@tsunningwah3471]

always feel like 'I know how to use the tool without knowing why they worked'

[@douglasstrother6584]

"Substitute" ~ The Who

[@yepitsodex]

great once you get into the meat of it, but the opening scenes in these always have no bearing on why you would use these methods and are never mentioned again... would be perfect without that great work

[@sanelprtenjaca9147]

This is mathematics.