How to use Laplace Transforms to solve HARD integrals
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- Опубликовано: 5 апр 2020
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Blackpenredpen Blackpenredpen (+ C whoo)
He's a calculus teacher, uses black and red.
He does math for fun (integrals), diff eqs get done.
Usin' complex numbers, doin' marathons.
And as always, that is it.
*specials thanks to Zach and Jonah for your amazing work!*
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Q: what’s the integral of (cos(at)-cos(bt))/t from 0 to inf?
ln(b/a)
@@juanmanuelmolanobaron7385 yes
ln(b/a). Can you make a video demonstrating the parametric equations of the Cissoid of Diocles?
Thanks so much for the opportunity to write this song! We had so much fun making it :) And another great video as always!
Jonah Sussman
I should be the one to say thank you! Thank you Jonah and your brother for your time, effort and creativity! It really put a smile on my face when I heard this yesterday! Thank you!!
Awesome song guys! Love the ad libs in the background... reminds me of migos
chico baber thank you! :)
Omg that outro song lmao
😊
"life doesn't have to be that hard" - BPRP :D
It really doesn’t. : )))
@@blackpenredpen hey i really like your channnel very much.It helps me very much even though i technically only have calc 1(calc required for physics and chemistry of highschool) i still appreciate your content sir.Keep up the good work.
I have learned a lot of things from your lectures. You make complex things so easy and understandable. You are a great teacher indeed.
prof chow, thank you :D i love having calculus in my life, the videos lately have been really cheering me up
I am very glad to hear!! Hope all is well!
Goosh I was preparing for an exam in integration learning from your videos and here it commees
Well as an engineer, I really have to say I appreciate this video... Great work
Thanks!!
@@blackpenredpen you're welcome. Now that I'm under semi-quarantine I decided to start a channel to answer math questions by request. Feel free to check it out sometime
Wish you posted this videos on Laplace when i had the unit....hahaha cool stuff manh!!!!
As a university teacher, I really appreciate your way of teaching. Your scrupulous explanations are off the charts.
Just watch this Math Channel.. very impressive
ruclips.net/channel/UCZDkxpcvd-T1uR65Feuj5Yg
lifes so easy when i stay at home and just watch what all dis dude comes up with : )
Hello bprp I am a child of 14 from India and I love your videos
Sir you have shown us the derivative of f(x) = (x^x^x^x^...). Is this f(x) is integrable??? Wolfram Alfa can't solve the integration.
Pls discuss about this...
Abhirup Chakraborty not an answer but an observation. f(x)= exp[-W(-lnx)] where W(x) is the Lambert W function
closed form of that function is f(x)=exp(-W(-ln(x))) where W(x) is a Lambert W function. I think you can get integral of f(x) in terms of W(x), which is non-elementary
@Shimmy Shai The integral of x^x can be expressed with a nice series: www.desmos.com/calculator/m7l7pxpqwc
@@maxsch.6555 Thanks a lot... 😀😀😀
Shimmy Shai *The integral of x^x really needs - no, begs - to be its own special function.*
It really doesn't. There are virtually no applications for a function such as this, and there are no useful or straightforward generalizations you can build from this either.
That outro song was serious fire 🔥♥️🙌🏽😁😭
loved the song
Great ...
Thank you my lovely Teacher 💖
Hi! Where can i find examples or exercises of HARD integrals to solve with Laplace transfrom?
Hi, can you make a video demonstrating the parametric equations of the Cissoid of Diocles?
Could you do more Fourier series? My diff EQ professor stopped teaching.
nice song there
Yale NG thanks!!!
Amazing Content...
Damn this time I'm fast
Me tooo
Congrats 🎁🎁🎁🎂🎂🎈🎈🎀🎉🍌🍌🍌💩💩
Nice video, you're wonderful.
Hi from Italy🇮🇹
Just watch this Math Channel.. very impressive
ruclips.net/channel/UCZDkxpcvd-T1uR65Feuj5Yg
Not that I have time to play with it right now, but I bet Feynman's Technique would handle this pretty well too. Toss in a term of e^(-bte^t), which evaluates to 1 at b=0 and 0 as you approach infinity. Take the derivative and it poops out a term of -te^t, which will cancel out that pesky denominator. From there, maybe some integration by parts, then all the usual Feynman steps, and then we're done. Maybe? It might work.
Even simpler, just throw another variable into the argument of the cosine, say, x, and then differentiate with respect to it. Now you just have to integrate e^-tsin(tx) from 0 to ∞. Just apply IBP and then integrate with respect to t and you're done.
I was doing Laplace transforms today and yesterday and this appears while I surf through youtube.
Just watch this Math Channel.. very impressive
ruclips.net/channel/UCZDkxpcvd-T1uR65Feuj5Yg
Feynman’s Technique shall also work but it took me a good 35-45 minutes to solve. It’s a good math challenge though!
Feynman Technique ? Isn't that the same as Leibniz's rule for differentiation under the integral sign ?
@@ericsmith1801 yes it is! The procedure has both names
Eric Smith It is! You start out by parameterizing the integral and then take the partial derivatives.
Eric Smith Yes and feynmann isn’t as cool as you think
@@rhversity5965 -- using the Laplace transform is much simpler but it still requires a clever substitution, but still simpler over all.
Please blackpenredpen teacher can you give a proof of Wilson's theorem in the lesons of algebra
Awesome 💛💚💜💙
yo lets go nice theorems
Yes!!!!!
I like, that you always smile)
hmm, can i ask for u blackpenredpen .. where dstribution came from 🙏🙏 ..
So when do you use it , just for definite integrals?
now I know how to get common denominators
Blackpenred pen do you know vivani's theorem? I kinda get how it works but rly i don't know the use of it hope you read it >
I am watching this on your trig pillow 😉
Edit one day afterwards:Also outro music at 8:27
Aww nice!!!!
Great explanation 👌
Sir I need help in this volume integration problem , I struggled for hours in vain
This is the problem
the base of a solid is the region between the curves f(X)=(x^2) -1 and g(X) = 1-(x^2) and it's cross sections perpendicular to the X axis are equilateral triangles .find the volume of the solid. ( Ans is (16√3)/15)
The area of a triangle is bh/2. If the triangle is equilateral, then all three sides have measure s. Hence b = s. h can be found by doing some simple trigonometry on a 30-60-90 triangle, and it happens that h = s·sqrt(3)/2. Therefore, the area is given by [sqrt(3)/4]·s^2.
The base of the solid was described as being enclosed by y = x^2 - 1 and y = 1 - x^2, the curves intersecting at x = -1 & x = 1. These are your boundaries of integration. The measure of the base of the triangles is, therefore, given by (1 - x^2) - (x^2 - 1) = 2 - 2x^2 = 2(1 - x^2). Hence s = 2(1 - x^2). This gives s^2 = 4(1 - 2x^2 + x^4), and the area is sqrt(3)·(x^4 - 2x^2 + 1). This is the function you want to integrate. This is because, in general, you have to find the area of whatever the cross-sectional shape is (in this case, equilateral triangles), and express it as a function of x or y, by using the information given, and then integrate said area along the axis indicated.
Isn't it much easier to use that a primitive function to 1/u - u/(u^2+1) is log(u) - ½log(u^2+1) =...= -½log(1+1/u^2)?
but log u in + infin ?
is not 0
Hey. Could you try the integral going from 0 to pi of cbrt(sinx)dx sometime? I know it might be a long wait.
I'm not even sure there is a close-form solution to this.
Angel Mendez-Rivera This is a very weird graph, but I have done the maths, and there is an answer. I just want to see how he would solve it with x=0 to x=pi
Teacher ...
I love this sentence: *... Link, In the description for your convenience*
But unfortunately you don't use it any more!
And ... Thank you for this video ❤️
Can u please help me finding the integral of 1/(1-tan^2x) dx?
Sajjad Mridul 1/[1 - tan(x)^2] = cos(x)^2/[cos(x)^2 - sin(x)^2] = cos(x)^2/cos(2x). It should be noted that cos(2x) = cos(x)^2 - sin(x)^2 = cos(x)^2 - [1 - cos(x)^2] = 2·cos(x)^2 - 1 implies cos(x)^2 = [1 + cos(2x)]/2, so cos(x)^2/cos(2x) = [1 + cos(2x)]/[2·cos(2x)] = sec(2x)/2 + 1/2. Integrating sec(2x)/2 + 1/2 should be much easier for you.
That shirt is great
Cosine Integral Function Sir could you please , thank you
More Integrals of same type please..............
Just watch this Math Channel.. very impressive
ruclips.net/channel/UCZDkxpcvd-T1uR65Feuj5Yg
Is it only me or are the links missing?
I want big board back!
WOW
sir
... What is your name.. ??
Why dont you try some Problems on Conics,It will be fun
bananas
8:32
Do a video how you switch red and black pens when when writing on the board 😂😂
There’s a video like this
Maybe... but normally 0
I think Feynman technique is indirect application of this technique
Just watch this Math Channel.. very impressive
ruclips.net/channel/UCZDkxpcvd-T1uR65Feuj5Yg
S=0 put karna tha
I solve this question in graduation
3rd
.
..
Anyone who got confused like me?
🥴🤯🤪
2nd
Isn't that too trivial ? HAHA
I'm early