Math for fun#16, I DIDN'T EVEN NEED MY GLASSES
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- Опубликовано: 2 окт 2024
- with integration by parts, DI method, • integral of (x^4/(1+x^...
integral of (x^4/(1+x^6))^2, with trigonometric substitution,
hard trigonometric substitution integral, hard trig substitution problem, hard calc 2 integral, math for fun #16,
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integral battles (just as fun): • integral battles!
blackpenredpen
math for fun,
follow me: / blackpenredpen ,
math for fun has hard math problem, challenging math problems, hard algebra problems, hard calculus problems,
I don't watch this for school or work, I haven't taken a calc course in 4 years. I watch this purely for fun.
wooow thxs for sharing even if we don't care :)
@@landgson1033 Seems like you cared enough to write a comment though.
Landgson I care
Lol same
@@glenjacobs423 eyy
RUclips need more educators like you. Very concise!
Hi, from philippines :)
Emerson Ruiz Rico thanks!
I love your enthusiasm! I kinda like you talking fast, I managed to follow it. Brilliant, keep it up I love your vids :)
Adam Jones thank you !
Exactly. I usually play youtube video's at 1.5x speed but your talking speed is perfect at regular speed. Keep up the fun video's :)
math on stereoids
OR
math on meth
I'm sorry.
Why is this so friggin' fun
"Hopefully you are BADASS enough to do this in your head" hahaha
We can also use substitution y=x^3 And for integral y^2/(1+y^2)^2 method by parts ( this integral is(-1/2)*integral (y*(1/(1+y^2))'dy)
It's more easy for partial fractions resolution.
Love the vid, also can’t get over the tan line from your glasses haha
RUclips Recommendation Are Getting Better Day By Day
Integration Teaching Of This Quality Will Surely Increase Ma Grades
You Are 🔥 Sir !!
Glad to hear. Thanks and best wishes to you.
It all turned out so nice
This is too beautiful
I think that using the hyperbolic fonctions it's easier by substituting x^3 with sinh(x), but your trick is really cool and I really like your energy
Hi from France !
Nice sir.
You make me love math even more!
Bro solved this in 7mins
Me: more like 30++...🤣🤣🤣
Easier done by DI method. x^8 on numerator => differentiate x^3 and integrate (x^5/(1+x^6)^2).
Yes you can do that by performing integration by parts.
Very nice integral! Just being able to spot the useful substitutions is my main problem in these kinds of integral. Nice videos as well. 😁
Don’t even know how to do trig sub but I feel like I’ve learned all I need to about it by watching this integral 😂
I have resolved it, but whith hyperbolic trig sub and parts, but finally it is the same
Found it but I changed the variable 3 times 🐸💔
Excellent job .
This speed is a lot better, otherwise it would get boring.
dude you are the integral god
We can also take x^6 common from Dr
Then take x^-3 as t and substitute
Can you elaborate why you can replace on X^3 bei tan (theta) and leave the other x^8 untouched ? that one I am missing the point?
Now I can *blindly* follow you.
vry difficult and lengthy
6:39 Are you a bad enough dude to rescue the hypotenuse?
sinx cosx = tanx (cosx)^2 = tanx / (secx)^2 = tanx / ( 1 + (tanx)^2)
Back in my Calc I class we used to find a relationship between tan(t) and sin(t) using the trig formulas, prof included, but you just draw a triangle every time and call it a day. I wish I knew this channel when I was in college
I mean formulae is easier than triangle in my opinion
6:41 badass!
from6:00~
sinxcosx
=sinxcosx/(sin^2x+cos^2x)
=tanx/(tan^2x+1) (divide denominator and numerator by cos^2x)
=x^3/(x^6+1)
(tan)^-1 it is arcus tangens (arctan) in my country....
Could you solve this problem using partial fractions? The denominator factorises to become (x^2+1)(x^4-x^2+1)?
Hii...I am big fan of your teaching style .. Respect from India..
The best
really good
Eashaan Singh thank you
Trig sub is satisfying ❤️❤️❤️
why don't we substitute 1-cos^2(thita)? for the sin^2(thita)?
Plis integral ((e^ax)/(x^2 +k^2)) from -inf to inf
You have two different Math for Fun videos labeled #16. This one isn't even in your Math for Fun playlist, while others there are not given a sequence number in the title.
May I ask how you have so much energy. What is your secret. At this point in my life I wake up tired. Seems like I was just born tired
Just awesome - you make learning math so very interesting. I just love all your vids. Great show - keep enthralling us with these lovely vids.
mohan153doshi thank you!!!!!
Can you do a video on solving the indefinite integral, from 0 to infinity, sin(x^2) dx or sin^2(x) dx
Djdjcjcjcj Jfnfjfidnf this does give me a lot of information I do appreciate this alot! I am only 14 so this is great help. thanks!
18 people dislike why? what's wrong
Your enthusiasm is contagious! Very good content 😁
Hi dude i from indonesian i very like u kwwkw
Next video I’m watching twice as fast
I watch this because an Ood is teaching math, only a whovian will understand.
HOW COULD U POSSIBLE SEE THAT MANY STEPS AHEAD CALC IS RIDICULOUS
Michael Ossorguine lol not really pretty straightforward once you've learned
Most people wouldn't try and do it in 7mins with no thought, blackpenredpen is just a legend. Also, probably planned the video ahead. People overemphasise the importance of natural intelligence in mathematics. Practice (hard work) and memory/knowledge is also very important.
Just need to go one step at a time. Seeing (1+x^6) means that one uses a trig substitution with tan for x^3. After that, work it all out and let things fall where they may.
when i see the problem, one thing i know is to use it with trig sub. we have the same answer.
W/out the glasses u kinda look like me and I'm 12 XDDDD
Not a lot tho
How did you ever guess what substitution to make?
pleas help me integral (e^5x)/(3x+1)
You are the best I have seen.
Thank you so much for a great job.
How is letting x^3 = tan theta a valid step, could someone explain please?
You could have theoretically chosen anything, it's a method called integration by substitution, in this case, tan theta was a good substitution to make as it allowed us to integrate it nicely,. In theory, you can choose anything to be your substitution as long as you change the limits (if definite integral) and ensure you are integrating with respect to your substitution (i.e change dx to dt or du or dtheta or whatever your substitution is).
Basically, it's just a technique used to manipulate integrals into more manageable ones.
Thanks so much, clears it up an awful lot! Just wondering, is it still valid to sub in either sin(theta) or cos(theta) given that they can only have a value from zero to one? Tan makes sense to me because it can have any value, or am I missing the point here?
It is still valid to sub in sin or cos, I don't know why though because I think what you're saying is a good point, might be a little bit out of my depth to answer that, but what I do know is that they're definitely valid, I think tan theta was chosen in this case not because it has no limits but because it cancels nicely with sec due to the identities.
that´s why you only do it in indefinite integrals this simply. here it´s simple, whatever floats your boat as long as you only do steps that dson´t change the value. (normal fraction rules) the fraction well ther integral must stay the same. as long as you can find something that is easier to work with and don´t change the value. that´s where the second variable comes in. itr´s just another variable and there will be some value that will fulfill the condition you set when you substitute. that´s why you integrate in respect to the new variable and change back later. you still solved the same integral but over simpler route. but that´s as long you have no limits. with limits its gonna get a pain in the arse to do it like that because you need to adjust your integration limits.
In the case of sin(theta) and cos(theta), you can still use it because sin^-1 and cos^-1 have Analytic Continuation in the complex domain. So those substitutions can take on the needed values with some complex-values of theta.
Sir do you have any facebook page?
Holy... it was incredible!!!
MajkG MajkG lol! Thanks!!
really it is interesting.
there are many cool integrals in our channel see them.
So cool how the answer is in exactly the same form even with a completely different method to the last video...
ToneWarz. Yea!
Reverse of tan ??? What the .... It should be arctan not tan^-1 which is cotan
It's standard to write arctangent that way. Any other number is the power, -1 is the exception.
You talk too quickly sorry!
that trick with finding cos and sin via triangle and tan just blew my mind! Thats just awesome!
Thanks very much sir
Sir your videos does not only provide us to solve any problem easily but also they provide us different and easy method to solve problems, thankyou sir
very helpful videos i got an A on calc 1 and 2 thankyou verymuch
It's nice got it some new👍
What method did u used sir?
this was awesome!!
You could almost toss a coin between Pi and a Trig in the answer - right?
The invert tangent is arc tan
tan^(-1)(x)=1/tan (x)
x=tan ( arctan (x))
this was insane
u r so amazing.I am held watching your videos the full day.love u so much
I AM BADASS ENOUGH!!!
Plz do this (1-9x²)/(1+x²)^6
Picked the wrong one to watch at 06.45a!
Can you please do a video on how to take the derivative of your final result? Thank You
Why did you use tan theta specifically for your substitution why not cos theta or even sin theta?
osama abdalla because of sec
So that he could use the identity 1+tan^2(x) = sec^2(x)
I am confused by the very last step where we combine square roots. Shouldn't it be sqrt(4x^6+4x^12) or 2x^3*sqrt(1+x^6) when we factor 4x^6 out and out of the square root?
You would be right but it isn't 4x^6 it's 1+x^6 written a little messy.
what the hell is theta
Well vídeo, Hi from Spain.
Jorge Lorenzo thank you!
i want to marry you
Sir I have question can you solve it . Please keep make solution in the form of vedio and explain to me.
Question :
(Integration of) ( (x^7)+2)/(((x^2)+x+1)^2)
Well with long division, partial fraction decomposition and trig sub you can solve this integral.
joseph barnes.
I'm calling it. He's a titan for sure.
yo man, slow down
forshee pious.
You are a machine sir. I hope you are managed to come up with your own theory
Excelente
In this integral i like more integration by parts
3:46 why did he write cos^2(theta)?
1/secQ = cosQ
Eres un PRO bro! Saludos desde Eciador...
Brilliant!
elmer reed.
Thanks..
god damn
hell nah
can anybody help me by sharing the link of the other video with the different result, please?
blackpenredpen yeah thank you!
Beast !
welcome
THAT'S GREEEEET WHAT AN INCREADIBLE IDEA
On the right side, are those double angle formulas? That's where I got lost. :(
yes, sin(2x)=2sin(x)cos(x)