Differentiation under the Integral Sign Tutorial

[Aelias]

Hey everyone! I've decided to start making videos again. Let me know if there's any topic you want me to cover in anything related to math, physics, or engineering.

[hemanthbhaskar]

Paige is perfect.... She's making me learn new complicated

[dallinrichards]

a math video using LaTeX? I need more of these!!

[domc]

there seems to be a relatively scarce amount of info on this topic so thank you for shedding light on it with some worked examples. this has been added to the tool box

[erockromulan]

This video helped my group tremendously for a graduate fluids problem. Thank you!

[kingbeauregard]

Really solid video! The situation that makes this technique the most insane (yet helpful) is when you introduce a factor of "1", and by "1" I mean something like "e^(b(x-2))" evaluated at b=0. That's a crazy way to generate a term of "x-2" through sheer force of will.

[marcusrosales]

The second one can be done by breaking up the integral from 0, 1/n, and infty.

First part isn't linear but goes to zero if you send n to infinity (just a Taylor series). The second bit is linear so distribute integral to both the terms, reindex and cancel what you can. This method works in more generality for any exponents. Like -ax and -bx gives an answer of ln(b/a).

[madvexing]

Hey, perhaps I'm a little late to this video. Just wanted to say thank you very much for such a simple video about this topic. since other explanations I have found have been too complicated for me. Now I can take on this sort of stuff with (relative!) ease compared to before!

[naifkhan]

your way of explaining is really great good job

[Metalhammer]

Just a small tip. Instead of testing for the constant of integration in the last step you simply can use the fundamental theorem of calculus you know
f(x)=int o to x f'(t)dt
And substitute the original value of b (2 in the first integral or 7 in the second) in the upper bound and solve that definite integral.

[themathaces]

You can use \partial instead of \delta for partial derivatives.

[seanclough]

I like the fancy font versus white/chalk board scribble. I guess I'm slower than others (processing time of information) and would ask you to slow your syllabic cadence. I can follow this at a slower pace and it's new, interesting. You obviously know your stuff and I thank you for this post. I don't know when I'll ever need to integrate sin(x)/x where x is [0, inf) as a math hobbyist but this stuff is kinda fun. Thank you for you contribution to free education!

[leifefrancisco]

You made a video explaining something no one else could

[BeniBoyzGuitarSlamz]

Wow. Thanks a bunch, super helpful video. Will have a think of topics I'd like you to cover.

[kovanovsky]

This is a mind blowing technique! Thanks!

[rajivnarayan]

Needed this for fourier transformations thank you

[engr.tonystark]

This helps! I am currently pursuing computer science and engineering...I got perfect at my calculus 2 test because of your video...thanks!

[arjunmodia]

Thanks a lot dude, you cleared a great doubt of mine.

[AdityaKadamMechanical]

You explained so clearly. Thank you Bro's :)

[babhishek]

its pretty very simple to solve im hoping to over come with some mor examples..thank you