Leibniz Integral Rule - updated! 💪

Рет қаралды 3,870

6 ай бұрын

Prove the Leibniz integral rule in an easy to understand way. The Leibniz integral rule brings the derivative right inside the integral. It is useful in solving hard integrals such as the ones below:
• Integral of e^-x^2 usi...
• Integral of sinx/x fro...
• Integral of x^100e^-x ...
Hungry for Integrals? Check out:
• Hard Integrals

Пікірлер: 13

@daviddecazanove1138 7 күн бұрын

Ok, I had to wait and watch till the end to have my answer.

@fourier07able Ай бұрын

Excellent explana🎉tion of this Profesor for Liebniz's Integral Rule. It basically requires of the derivative definición, mean value theorem for Integrals, squeeze theorem and Lebesgue's dominated convergence theorem. But the descriptive graphics are Pretty nice!

@dohyun0047 4 ай бұрын

neat explanation thanks

@daviddecazanove1138 7 күн бұрын

I understand the rest but I really do not understand how a and b are functions of t.

@dohyun031 5 ай бұрын

Amazing video for this hard theorem! I have always wondered how people were able to just switch differentiation and integration. I have one question though, when you apply the Lebesgue's Dominated Convergence Theorem at 9:41, what would be the dominating function g(x)? Can I put g(x) as f_t(x,c)*h for c in (t,t+h)?

@daviddecazanove1138 7 күн бұрын

I do not understand the variables along the x axis that changes as t to t+h!

@user-lz5jj4nz3g 5 ай бұрын

Thank you😂 i finally got it

@daviddecazanove1138 7 күн бұрын

Is there a relation between x and t or are they independent?

@gentlemandude1 Ай бұрын

Great video! What are you using to make the animations?

@brainynerdtutor1626 Ай бұрын

Thanks! I use PowerPoint or Keynote for animations and free applets for graphing and simulations.

@alfazero1423 6 ай бұрын

Thanks for clarifying this hard topic. Very nice explanation. but some steps were a bit confusing like 1. at f(c)(b(t+h)+b(t)) in MVT you write as f(c,t+h)(...)...why f(c,t+h) not f(c,t) for example.

@dohyun031 5 ай бұрын

I also agree. At 5:39, I think the correction would be f(c,t+h)(b(t+h) - b(t)) instead of f(c)(b(t+h) - b(t)). Besides, the reiteration of the MVT in the next slide at 5:53 should be f(c,t+h)(b(t+h) - b(t)) instead of f(c)(b(t)-b(t+h)).