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Integration by substitution (visualised)

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Integration by substitution is one of the most powerful tools for combating integrals! It allows us to transform a difficult integral into a significantly easier one. In this video we visually show what actually happens when you perform a substitution and how to properly use integration by substitution.
Integration video: • Integration
Problem Sheet: mathacy.com/pr...
Timestamps:
0:00 - Intro
0:37 - Integration by substitution
1:30 - Visualizing integration by substitution
4:12 - Examples (Cancellation)
5:27 - Examples (Substitution for composite functions)
6:04 - Examples (Both)
7:07 - Penalties

Опубликовано:

14 авг 2024

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Комментарии : 42

@aleenavirdee5656 3 года назад

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!

@okayokays9926 3 года назад

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

@aaronnanoo1887 3 года назад

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

@vathanagopinath8466 3 года назад

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!

@Abdullah-kw6kk Год назад

All of this for free; amazing and much appreciated

@aromeran 2 года назад

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

@rektlzz7808 3 года назад

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

@Veptis 2 года назад

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 RU-vid 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 Год назад

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

@iplgeek 3 года назад

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

@BhavdeepSoor 3 года назад

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

@cynthiako94 3 года назад

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

@navneetkaur2445 3 года назад

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

@nikkibhamra7536 3 года назад

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

@DiLLZGFX 3 года назад

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

@DamianWaynes Год назад

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

@user-lq1cs3vi9z Год назад

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!

@indisingh2990 3 года назад

Great explanation about integration love the visual.

@punditgi Год назад

Brilliant! Best explanation anywhere! 😃

@Bedoroski 7 месяцев назад

Great work.

@skaur6838 3 года назад

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

@lukollolak6219 2 года назад

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

@janhavikulkarni9893 3 года назад

This is was so well explained!!!

@justadreamerforgood69 Год назад

You're a snack 🥨

@m.d.asgarmansuri5731 Год назад

Thank u so much for your fine work

@vaaniakapooronbehalfofaliz2187 3 года назад

Super informative! Love the visuals

@Dinesh123lol 3 года назад

Amazing video, very clear explanation. Thank you!

@IlIlllIlll Год назад

Thank you so much for this visualization

@AbdulAziz-fg2cy 2 года назад

beautiful ANIAMTIONS

@Elvisitante Год назад

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

@alifrahman7099 3 месяца назад

Amazing!

@sukhibhamra5750 3 года назад

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

@nhatkhang7363 Год назад

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

@lindie5830 11 месяцев назад

I also found this to be a jump

@ShuyuLin-sh2gk Год назад

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

@zyggzag4154 Год назад

Thank-you! legend!

@josealejandroconstantinola7520 2 года назад

Sir what application ypu used in this presentation?

@tsunningwah3471 7 месяцев назад

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

@douglasstrother6584 Год назад

"Substitute" ~ The Who

@yepitsodex Год назад

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