Leibniz Integral Rule - updated! 💪

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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 ...
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• Hard Integrals

Опубликовано:

30 сен 2024

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Комментарии : 15

@dohyun031 7 месяцев назад

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 2 месяца назад

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

@daviddecazanove1138 2 месяца назад

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

@mirimonganizitheodore3911 12 дней назад

I like the shirt

@daviddecazanove1138 2 месяца назад

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

@minhnam3827 Месяц назад

great !!!

@dohyun0047 6 месяцев назад

neat explanation thanks

@fourier07able 3 месяца назад

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!

@gayecelebi8975 6 месяцев назад

Can you suggest a book for understand clearly feynman's trick&Leibniz's Rule clearly please?

@daviddecazanove1138 2 месяца назад

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

@alfazero1423 7 месяцев назад

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 7 месяцев назад

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)).