When I first saw this, I was thinking “yeah this has to be joke.” We all know that π = e so the answer is 0. The hardest integration boi is obviously the integral of the square root of tan(x).
Using a whiteboard instead of a blackboard, The Gordon Ramsay of Mathematics would call this "Disgusting" and I would too. Even though it is the first of april, how could you break my heart like this?
Euler’s formula is the following: e^ix = cos(x) + i sin(x) If you plug in some imaginary number: e^(i*ni) = 1/e^n = cos(ni) + i sin(ni) e^(i*-ni) = e^n = cos(ni) - i sin(ni) You can manipulate this to find the individual components of the formula, similar to their hyperbolic definitions: (1/e^n + e^n)/2 = (1 + e^2n)/2e^n = cos(ni) (1/e^n - e^n )/2 = (1 - e^2n)/2e^n = i sin(ni) To find sin(ni), you can use the Pythagorean identity and substitute in cos(ni) (I will replace the square root of x with “sqrt(x)”) sin(ni) = sqrt(1 - cos^2(ni) = sqrt(1 - ((1 + e^2n)/2e^n)^2) The denominator will be the same if you make these fractions like, so you can take its square root - the square root of something squared will be the argument. If you expand out the numerator, you can use the binomial theorem: -1 + 2e^2n + e^4n = -(1 -2e^2n + e^4n) = -(1 - e^2n)^2 Putting this back into the original expression and using the commutative properties of the square root, you get this: sin(ni) = (sqrt(-(1 - e^2n)^2))/2e^n = sqrt(-1) * (sqrt((1 - e^2n)^2)/2e^n) = i * ((1 - e^2n)/2e^n) = i sin(ni) This causes a contradiction and implies that Euler’s formula does not work for any number of the form ni, but I have been wondering if n could be imaginary. In that case, would that cause a paradox? This all confuses me, so I wanted to ask. Trigonometric functions on i confused me in the first place anyway. Thank you for taking the time to read this big block of text (if you do!). Sorry, I know this isn’t related to the video but I thought it would be nice if you did look at this. From an 11-year-old fan (sorry if I sound like a brag about that). P.S. I put this comment on another video but seeing as you hearted me (thanks) I thought you might see this one. I’ve honestly been wondering about this for a while. Thanks anyway
This seems oddly familiar. dId YoU ReCyCLe YOur apRIl FOOls ViDEo agaIn? Yes you did and 2021 will be the same if Coronavirus doesn't eradicate humanity before. xD
THIS IS WHAT I GET UP IN THE MORNING FOR.
you have pretty low standards then ngl xD
@@PapaFlammy69 you can't blame me, it's integral to my day.
it's 10 o'clock here
I totally think I never watched this before, so definitely, it was worth getting up for it today. Also 10:23
@@PapaFlammy69just wanted to tell you that you've finally transformed into a demon
When I first saw this, I was thinking “yeah this has to be joke.” We all know that π = e so the answer is 0. The hardest integration boi is obviously the integral of the square root of tan(x).
Saaame
But..but.. what about this? math.stackexchange.com/questions/562694/integral-int-11-frac1x-sqrt-frac1x1-x-ln-left-frac2-x22-x1
What about the cube root of tan(x)?
Mom can we have a mathematician?
Mom: No there is mathematician at home.
The mathematician at home: 4:58
xD
Alle Jahre wieder meine lieben Kinder :^)
100k subs, congrats 🎊🎉🎉
And every year from now on Papa 🙏 😊
Du kannst kein Mathe. Wiederhol mal lieber die 2. Klasse und lern dort zu integrieren m8
I'm mad that I can't speak gehman
Last time I was this early I got divorced
bruhv
@@PapaFlammy69 Papa replied to my comment. I can die happy
I know this person. He was never married.
@@silentinferno2382 Just because you have a girlfriend doesn't give you the right to flex Antimonium. It isn't fair to us weebs
Antimonium Heptadiene oh no he was exposed
It's approximately equal to 0.138904i which is approximately 0. QED
yeyeeee
Oh dear, I think slamming into the blackboard earlier on has taken its toll on Our Good Fellow.... Lol
xD
Lol yeah
The answer is zero because the domain of that horrible function is "[-1,1)"
Tale 0 out of the domain
How could I not have seen this
Just as always, this is art.
Looks like someone hacked his channel again for April Fool's Day
nahhhhh
2 uploads in one day man! Cheers for the mathematical prowess man.
But papa, according to the fundamental theorem of engineering e=pi, therefore the integral equals to 0?
yeye
Very educational!!! still trying to wrap my head around some steps of your integration, but all 46 minutes of the video were worth watching ❤️❤️
xD
I'm wonder if this video is wondering if this video is wondering if this video is wondering if this video is wondering if?
Just for fun I had to look up this integral to verify... It turns out one source reported the answer to be a complex number.
I thought you'd been social engineered again until I realised the date
for april fools next year can you actually solve the integral but convince your viewers that you won't solve it
That decomposition in 0:56 have a spcial name or something?
nah
It is called a + b - b = a
Hecking super congratulations mah boi
I got the notification for this div 5 mins ago exactly. It's 2:56 on April 2nd
Using a whiteboard instead of a blackboard,
The Gordon Ramsay of Mathematics would call this "Disgusting" and I would too.
Even though it is the first of april, how could you break my heart like this?
Except that Papa Flammy is never undercooked!
*Ramsay
@@MathNerd1729 oopsi XD
Thx Mate
@@janus3042 You're welcome
Happy Inegharals Day!
Also, why is the video still at maximum 360p, it is so unfair?
ye
That was an Apr fool. I wasted my net to download it.
edit wtf happened after 5:00
But π=e so the integral is equal to 0
ye
I should've just watched the video first xD
@Sebastian Henkins I did. But I commented this almost as soon as the video came out.
@Sebastian Henkins But by the piano axioms, e=2+1 and π=3, so π is the succesor of 2, which by definition is e, therefore π=e. QED
@Sebastian Henkins But I proved the theorem by proof by calculator
Today's my birthday, and this is the best gift. Thank you flammable maths.
Happy bday my son
Thank you
OMG you DID use theorem of engineering!! I laughed so hard hahahaha I knew it
This is beautiful lmao. Congrats on 100k subs m8
thx Ricardo
No problem flammy ma boi keep up the good work!
your new profile icon is so clean!
thx! =)
ayy 100k congrats Papa Flammy
Only an absolute madlad can put same thing in all the options for voting.
:D
e=pi ????? LMAO XD XD
FTE
@@nanigopalsaha2408 excuse me? what is mean?
@@거미남자_spidy The Fundamental Theorem of Engineering
@@nanigopalsaha2408 ah yeah In Engineering mathematics, like you said, Pi is considered as three. XD XD
I can't believe I felt for that one again. Last year was the same thing LOL
xD
Where did it all go wrong?
Euler’s formula is the following:
e^ix = cos(x) + i sin(x)
If you plug in some imaginary number:
e^(i*ni) = 1/e^n
= cos(ni) + i sin(ni)
e^(i*-ni) = e^n
= cos(ni) - i sin(ni)
You can manipulate this to find the individual components of the formula, similar to their hyperbolic definitions:
(1/e^n + e^n)/2 = (1 + e^2n)/2e^n
= cos(ni)
(1/e^n - e^n )/2 = (1 - e^2n)/2e^n
= i sin(ni)
To find sin(ni), you can use the Pythagorean identity and substitute in cos(ni)
(I will replace the square root of x with “sqrt(x)”)
sin(ni) = sqrt(1 - cos^2(ni)
= sqrt(1 - ((1 + e^2n)/2e^n)^2)
The denominator will be the same if you make these fractions like, so you can take its square root - the square root of something squared will be the argument. If you expand out the numerator, you can use the binomial theorem:
-1 + 2e^2n + e^4n = -(1 -2e^2n + e^4n) = -(1 - e^2n)^2
Putting this back into the original expression and using the commutative properties of the square root, you get this:
sin(ni)
= (sqrt(-(1 - e^2n)^2))/2e^n
= sqrt(-1) *
(sqrt((1 - e^2n)^2)/2e^n)
= i * ((1 - e^2n)/2e^n)
= i sin(ni)
This causes a contradiction and implies that Euler’s formula does not work for any number of the form ni, but I have been wondering if n could be imaginary. In that case, would that cause a paradox? This all confuses me, so I wanted to ask. Trigonometric functions on i confused me in the first place anyway. Thank you for taking the time to read this big block of text (if you do!). Sorry, I know this isn’t related to the video but I thought it would be nice if you did look at this. From an 11-year-old fan (sorry if I sound like a brag about that). P.S. I put this comment on another video but seeing as you hearted me (thanks) I thought you might see this one. I’ve honestly been wondering about this for a while. Thanks anyway
5:26 didn't know jigsaw interchanged integrals. Good to know.
100k subs! congrats!
Happy April's fool papa!
Now from -1 to +1 ;)
YAY 100,000 flim flams
:)
Why is this 3 years ago
Oh wait
Bro 50 minutes!? I just plugged it into my calculator smh...
sheeesh there are actually 2 bad bois in this video :OO
I think therefore pi=e
This is a special kind of asmr
Thank you for the video! All of you friends are super awesome! Oh, moments with this video are sad.
Happy new month
i'm so confused lmao
3:03 sums up this video
What else could I have expected
xD
get happy april fools m8 to 69% pls
This fever dream is amazing
jens, you are BA in math and BA in physics too ?
Master of Education in Maths, Physics and Pedagogical Studies
If it ain't broke don't fix it.
I feel violated c: oh ye
rip
Elementary haha, just 0 obviously. Integral from 3 to 3 is always 0.
exactly:^)
I was legit about to watch the whole video as well...
who tho?
Congratulations 🎉!
I mean I'm gonna watch it but if it turns out it's a 45 minute April fools joke I will be very sad
xD
ppppppppppppffffffffffffffffff
thats ez pi=e so that integral obviously =0
WAIT WHY ARE U AT UR OG WHITEBOARD
ayyyyyyyyyyyyyyyyyyyyyyyyyyyy lmao eks DDDDDD
:DD
wait u acc said that lmaooooooooo
Just press ctrl + alt + downarrow for the last part of the video
Though... idk who actually wants to watch it.
46 mins lets fμcking go
edit: oh.
xD
Thats mammoth
Good April fool
Dude this is way too many ads
xD
Thank you!!❤️🔥
Is e really equal to pi ??don't think so
I
thought you got hacked again bruh
nahhhhh
Review time
This seems oddly familiar.
dId YoU ReCyCLe YOur apRIl FOOls ViDEo agaIn?
Yes you did and 2021 will be the same if Coronavirus doesn't eradicate humanity before. xD
:D
Not againnnnn
xD
Wow
360p poggers
ezzzz
WTF!
0 easy, using the basic fundamental theorem of engineering that e = pi.
Fuck you already did the joke, now I'm sad : ^)
(^:
Oooold!
Wait a minute, who are you?
ye
40mins😮😮daaaamnnn
100k
V:
you have thieved a video from your past self. even worse than thieving from the hacker
what the fuck
666
e pi +c
First time i am this early
Are you just want to waste the time of viewers?