doing this type of solutions is bad, even if trolling.. your brain will actually start thinking in that way. which is bad. just look for the best algorithm to apply to your problems instead. i bet its more fun :D
A similar one was on my complex analysis final exam, it asked to find the integral from -inf to inf of x*sin(x)/x^2+1, surprisingly the result is the same, pi/e. Amazing!!! But to show that Gamma tends to zero as R tends to inf I just used Jordan's Lemma hahahaha
Very nice video. I like that you get to the point quickly in your videos. By the way, the integral where you write the limits as R to -R is a poor notation in my opinion because the integral depends on the path. In particular, if you take a (continuous) path from R to -R that crosses the imaginary axis somewhere between i and -i, then the value of the integral is -pi/e instead of 0 (for those who don't know).
I am so proud of myself - I spotted a mistake at 14:01. You state the value of the whole integral is independent of the limit for R. This is not a 100% true. The residue needs to be contained in the contour. Hence R must be bigger than |i|=1. So the integral can turn out to be zero for R
Another crazy integral: What is the integral of sqroot(sinx) from 0 to pi? I found it 2√(2/π)(gamma(3/4))^2 in wolfram alpha which seems very interesting.can you provide me the magical steps?
@@Josh-wb7ii but this one is pretty _neat_ : one fraction, one trig on top, one quatdratic on the bottom, integrating over the entire set of real numbers..
if i use cauchy’s principal value for integral -infinity to +infinity cos x/x = 0 i am getting a weird answer of pi/2(e^(-1) - e), which actually is negative. What have i done wrong? all answers appreciated.
Can you do a video on complex analysis. the only thing I know about complex analysis is that the integral of g(z)dz over the curve c where c is defined by the bound [a,b] and the function f is the integral from a to b of g(f(x))*f'(x)dx
This was the first method I saw used to solve this problem, and I thought it was the coolest thing I had ever seen at the time. I still love this proof to this day. It's so fun to teach, and is great at the end of a complex analysis course as a perfect demonstration of the important principles.
Hey I've a few things to say. 1)Pls do more videos on complex analysis! I really liked it and I'm trying to learn it from your videos. 2)This may be a stupid question but pls answer me (I'm new to contour integration) In this question, if u initially take f(z)=(e^(-iz))/(z^2 +1); most of the stuff remains the same, except that the residue at i now becomes e/2i. So the contour integral now equals πe. So, finally wouldn't the answer become πe? Where's the mistake here?
@@PapaFlammy69 Estimados @Flammable, por acaso tendrían videos explicativos de Integrales de funciones racionales entre limites infinitos.. multiplicados por seno y coseno por ejemplo ∫ [cosx /(x² + 1)²] dx de (-∞) a ∞
@@vallinathan623 Euler's number is e≈2.71. I posted this a while back when I was still an amateur to complex analysis. Your response is appreciated tho. As for the answer, it turns out that you cannot use the lower plane for calculating the integral since the inteɡral blows up to infinity as z→∞.
Why do you use the upper half of the complex plane? It is not clear how or why you choose the upper half of the complex plane. Please explain... Thank you..
me encanta la matemática, pero desde que veo tus vídeos mi gusto se a incrementado notablemente, me fascina ver que hay retos interesantes en las integrales, integrales que no podía hacer ni me imaginaba como hacerlas
That was what I was looking for! But there were some issues with the solution of this problem using Laplace transform as pointed out here: artofproblemsolving.com/community/q1h1621189p10146292 Also, plz solve the integral posted by Kent Merryfield on the same page. I am stuck on that one.
I remember watching this for the first time and not understanding anything. Now I’m finally studying complex analysis and I understand everything :)
Same!
One day that will be me too
same as me rn :)
This autumn :D
I love how the humor and commentary is integrated (no pun intended) as you walk us through the solution. Well done!
Could you make a video of integrating x dx in the most hardest and inefficient way possible?
Let u = ln((3^x^4^x^i)/e^e^e^x)
This could be a ‘fun’ substitution to make ...
Please do this!
doing this type of solutions is bad, even if trolling.. your brain will actually start thinking in that way. which is bad. just look for the best algorithm to apply to your problems instead. i bet its more fun :D
@@mk-nw4si Who cares if its bad for you. Its fun!
@@David-km2ie yeah well.. but if someone does it often even if ironically it will just turn into a habit
real boi + curvy boi = real curvy boi ;)
A similar one was on my complex analysis final exam, it asked to find the integral from -inf to inf of x*sin(x)/x^2+1, surprisingly the result is the same, pi/e. Amazing!!! But to show that Gamma tends to zero as R tends to inf I just used Jordan's Lemma hahahaha
I am literally in love with this man tbhhhhhhhhh
Flammable Maths senpai noticed me
"And now we need to take a look for the poles...."
- Someone's FLAMMABLE grandpa,
September 1st, 1939.
Very nice video. I like that you get to the point quickly in your videos. By the way, the integral where you write the limits as R to -R is a poor notation in my opinion because the integral depends on the path. In particular, if you take a (continuous) path from R to -R that crosses the imaginary axis somewhere between i and -i, then the value of the integral is -pi/e instead of 0 (for those who don't know).
You're right, the notation was a bit confusing. I was confused for a while
Do more complex analysis videos, please! They are fun to watch and there is not that much of them on youtube.
I think your videos are great!....You have enormous enthusiasm and a great sense of humour....keep up the great work.
Hey , i don't know how to integrate on a complex plane and stuff uve done and contour stuff,so please can u make a video explaining these things.
Housam Kak. There is a nice book in The Schaum outline series ‘Complex Variables’. You’ll know it in 1 month.
now I do, this is really old!! and GOLD!
Hi, at 8:10 where did the ( e^i*phi ) disappear? before the integration variable d phih, there was ( e^i*phi ) , where did it go?
But the absolut value of this is also just one
You're freaking hilarious!! (And brilliant too)
That first contour integral sign you drew. Beautiful.
You explained it excellently. Even a dumb like me got everything except, why did we replace cosx by e^ix🤔🤔
He made complex analysis so simple that my mind is now being complex at everything
Now solve this integral
cos(nx)/(n+x^n) from -inf to inf
i did partial fractions just for fun at timestamp 13:37 R/(R^2-1) = R/2(1/(R-1) - 1/(R+1)) = 1/2*(1/(1-1/R)-1/(1+1/R)) ~~ 1/2*(1/1 - 1/1) = 0
Great video thanks Flammable Maths!
I am so proud of myself - I spotted a mistake at 14:01. You state the value of the whole integral is independent of the limit for R. This is not a 100% true. The residue needs to be contained in the contour. Hence R must be bigger than |i|=1. So the integral can turn out to be zero for R
I don't think it matters since we let R approach infinity anyways
I see, so the residue theorem is the easy part, the hard part is make the curve path vanish when R approaches at infinity
nice approach btw
Another crazy integral:
What is the integral of sqroot(sinx) from 0 to pi?
I found it 2√(2/π)(gamma(3/4))^2 in wolfram alpha which seems very interesting.can you provide me the magical steps?
Check papa's latest video on the beta function, that should give you an idea on how to approach the problem
I love ur complex analysis videos the best
I'm not familiar with complex analysis but I still enjoy this =)
Yes, thanks to your videos, I (a freshman) got to solve this 😎
Subscribed!
Actually I subscribed a long time ago!
Well deserved my boi!
I have no idea what’s happening but I like it.
(About to become an undergraduate student studying Maths so I’m in year 13)
why do you use exactly this new complex function , couldn't you use an other function at 0:46 ?
because Re(f(z)) = the original integrand
But why is it pi/e, I mean, math says so, but why....
It's just 1 tho
Because math.
@@YitzharVered _shut up engineer_
You could find infinitely many integral representations of whatever wacky combination of the transcendentals you wanted, it’s nothing significant
@@Josh-wb7ii but this one is pretty _neat_ :
one fraction, one trig on top, one quatdratic on the bottom, integrating over the entire set of real numbers..
Nice and correct solution... I solved it by the same way... I love very much complex analysis
I've thoroughly enjoyed this three part series. What's on the horizon for Flammable Maths?
Rewatching papa's complex analysis vids...
Great channel! It didn't take me a full minute of your content to press that subscribe button. :)
Thank you sooo much. This was beautiful.
if i use cauchy’s principal value for integral -infinity to +infinity cos x/x = 0 i am getting a weird answer of pi/2(e^(-1) - e), which actually is negative. What have i done wrong? all answers appreciated.
It seems that integrating cos(x) is fine when x is real, but when extending the domain to complex numbers you need to use Re( e^iz ) instead.
I love your videos, and the funny thing is that I don't even understand them.
You unconsciously accumulate all the knowledge of Papa Flammy so you also learn everything :3
Please antiderivative of f(x)=lncosx
hi! please what is the name for this integral ? I have this exercice : ∫ cos(t) / (t^2 + a^2) dt
Can you do a video on complex analysis.
the only thing I know about complex analysis is
that the integral of g(z)dz over the curve c
where c is defined by the bound [a,b] and the function f
is the integral from a to b of g(f(x))*f'(x)dx
We can do this thru feynman also
could you do this sum by cauchy residual method pls... putting cosx=(z+1/z)/2
This was the first method I saw used to solve this problem, and I thought it was the coolest thing I had ever seen at the time. I still love this proof to this day. It's so fun to teach, and is great at the end of a complex analysis course as a perfect demonstration of the important principles.
li_ as r-> inf
Hey I've a few things to say.
1)Pls do more videos on complex analysis! I really liked it and I'm trying to learn it from your videos.
2)This may be a stupid question but pls answer me (I'm new to contour integration)
In this question, if u initially take f(z)=(e^(-iz))/(z^2 +1);
most of the stuff remains the same, except that the residue at i now becomes e/2i. So the contour integral now equals πe. So, finally wouldn't the answer become πe? Where's the mistake here?
Reply pls?
Integral of 2xln((3x^2+4x-2)/(√(4x-1)) with respect to x.
Have fun with this L O N G boi
I honestly went to this vid just to see how Chinese calculus is.
The german accent+The great content+Calculus+great explanation=
*_THIS VIDEO_*
:)
@@PapaFlammy69 Estimados @Flammable, por acaso tendrían videos explicativos de Integrales de funciones racionales entre limites infinitos.. multiplicados por seno y coseno por ejemplo ∫ [cosx /(x² + 1)²] dx de (-∞) a ∞
can you please re-do this with cos^-1(x)?
What if we use e^(-iz) and use the same parametrization of Re^iφ. We get the residue as πe and not π/e or am I doing something wrong
@@vallinathan623 Euler's number is e≈2.71. I posted this a while back when I was still an amateur to complex analysis. Your response is appreciated tho.
As for the answer, it turns out that you cannot use the lower plane for calculating the integral since the inteɡral blows up to infinity as z→∞.
bro please do me a favour
solve int. tan^2(x)/(1+x^2+2x)
How about e/pi?
Best video 👌👌👌
who is the guy in the thumbnail?
Thanks. Now i recognise him :D I don't know why, but at first I thought it was Landau....but it couldn't be.
is it him, because Pál starts with the letter pi and Erdős with e?
@@csanadtemesvari9251 Probably not, but fantastic observation! !!!
Why do you use the upper half of the complex plane? It is not clear how or why you choose the upper half of the complex plane. Please explain... Thank you..
Mhmm so I could have used the bottom half as well? Since there is a pole there as well and residue theorem can be applied...?
Flammable Maths cool.. I really love your videos :) thanks!
I never understood why you can't use do contour integration directly without using converting cosine into a complex form
Why equal to Erdos?
I very much like your videos. In this one are you trying to make a point? In that case please share...
why do you like integrating so much tho?
Kaha se ho bhaiya jo aise bol rhe ho
Hey! We need some new integrals!
Integral of ln(x)/(1+x^n) dx from 0 to inf.
Can you help me with integral from 1 to 9 of [ln x]/x?
Great! Thanks. But is it possible to solve it like [ln x] is the hand around of ln x?
Good explanation, but please use a better audio setup. The echo makes listening to this hard. It makes it louder and harder to hear at the same time.
That's a boi right there!
Jordan's lemma is crying
best way!
Sir I have one problem plz give me solution
a siple application o the residue theorem could've made the ime spent solving this integral 4 ties less
FIRST COMMENT! PAPA FLAMMY, HAVE A FLAMMY DAY!! #NotificationSquadBois
Definitely with the help of some of Papa Flammy's Flammable Lasers!
Paul Ërdos
Soo.... = 1 ? By fundamental theorem of engineering
Why did this get recommended to me now?
impactante
me encanta la matemática, pero desde que veo tus vídeos mi gusto se a incrementado notablemente, me fascina ver que hay retos interesantes en las integrales, integrales que no podía hacer ni me imaginaba como hacerlas
residue theorem
Indai ke to nahi lagta ho
That was what I was looking for!
But there were some issues with the solution of this problem using Laplace transform as pointed out here:
artofproblemsolving.com/community/q1h1621189p10146292
Also, plz solve the integral posted by Kent Merryfield on the same page. I am stuck on that one.
HUH?!!? sneaky flammy where did u come from?!
Why do we need to study such complex mathematics? 🙃 (wondering this before my end semester exams tomorrow 🤣)
Lost me on that one... I'll have to read up on complex analysis...
Te amo :u
Bro i want to help u but i m poor ..sorry
He looks like Daniil Dubov
There is some mistake in it
❤️
You're always sayin' "my boys".... What about the girls? 😁
Your explanation is good, but your handwriting is not good. Please work on your handwriting to reach vast number of viewers.
Please antiderivative of f(x)=lncosx