Integration by substitution (visualised)

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.

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

[aleenavirdee]

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-kwkk]

All of this for free; amazing and much appreciated

[aromeran]

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

[aaronnanoo]

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

[okayokays]

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

[rektlzz]

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

[vathanagopinath]

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!

[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 YouTube 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

[cynthiako]

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

[DiLLZGFX]

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

[BhavdeepSoor]

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

[indisingh]

Great explanation about integration love the visual.

[nikkibhamra]

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

[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.

[DamianWaynes]

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

[ДмитрийСкрябиков-жэ]

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!

[lukollolak]

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

[punditgi]

Brilliant! Best explanation anywhere! 😃

[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 :)

[navneetkaur]

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