Integral of e^(ax)sin(bx) by using complex numbers (beyond calculus 2)

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Calculus tutorial on the integral of e^(ax)*cos(bx) and integral of e^(ax)*sin(bx), no integration by parts but we will use complex numbers. Whenever we have an exponential function e^x and a sine or cosine function, we can use integration by parts or this complex number method.

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Well ! Credit goes to Prof. Arthur Mattuck ! Who once said, "complexifying the integral is sometimes simplifying".

chandankar

I was literally trying to solve this one yesterday by integrating by parts... And it took ages. Thank you for the enlightenment. ^^

sofialpaca

Introducing i ("complexifying", nice!) to take a different route to the answer is a great example of how creativity is used in math. I know I'm not at a high enough level of understanding that I'd be able to come up with that method on my own. Great video, not difficult to follow even though the problem looks like it should be.

KyleJMitchell

I don't like to be on bottom.. I like to be on top.. 🤘special word's by Blackpenredpen sir... 😘

quantumcity

Huh what a coincidence! I was investigating very similar integrals today while trying to evaluate a problem that I’ve been working for a while. Also I can’t wait any longer for Fourier Transform :))

radiotv

I started watching your videos 3 years ago when I was still in high school. Now I’m studying mechanical engineering and I still keep coming back to watch them 😂

TheRandomGuyCOD

When I learnt this method in my further maths class I was shocked at how amazing it was!

JudeKennedyATCL

This really an incredible way to solve it, it was worth it subscribing to you and taking the time to watch ;)

mahmoodethiab

"i" don't like to be on the bottom, "i" like to be on the top.

AataFeraAshirvad

Cant believe my teachers never showed me this method... Thanks for the help.

Justin-ccbz

es increible que, aunque no hable ingles, pueda entender perfectamente por como haces paso a paso cada operacion. interesante video

lucasacosta

Yeahhh, Fourier Series!
Please show us the proof of 1+1/4+1/9+1/16+... = pi^2/6, using Fourier Transform/Series

weerman

I'm a noob and made them first "by parts" : it's not so complex !But I remembered then one of your previous video and tried this method : much more elegant, really !Thanks for this video and the best for 2019

egillandersson

Are we going to ignore 3:36 “I don’t like to be on the bottom, I like to be on the top” how funny is this line 😂😂😂😂😂😂

exoticcoder

"I don't like to be on the bottom, I like to be on the top"
HAhhhahhhahaahh!!!!

tonypalmeri

bprp : DONT DO INTEGRATION BY PARTS
me : let me try integration by parts

VaradMahashabde

i never liked integration by and your videos were so helpful, please make some videos for Special functions ( legendre, hermite and bessels )

rajivpandey

Yeeees ! My teacher insisted that it would be impossible to do it without IBP but I wanted to use Euler's formula...

sylvainpanneau

Steve, you taught a very easy way to integrate by parts in another video (method D I), so I found it much easier to use integration by parts using D I instead of the Euler equation. Your fault...ahahaha. I imagine that the method of the present video is really very important to get skill in Euler equation and Complex Variables, is that the case, Steve? Excuse my daring, but I suggest you explain in the commentary below the video the goal to learn the present method. Perhaps it would be a good idea to give more explanation in some other presentations, since the viewer can watch your presentations knowing better the main goals.I would like to congratulate you for your channel, excellent quality and I believe that you are contributing to give to people around the World a marvelous opportunity to learn, get motivation and like, or perhaps love Mathematics in advanced topics . Thank you very much for your effort to do that.

metabolismanimationandpoly

Nice video, really liked that integral!

waterfirecards

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