@@maths_505 I am not convinced. It comes close but it is not an ellipse. It has pointed edges. I tried it on Desmos. You can try for yourself too. I entered the following equations for comparison: 1) y=1/(1+acosx) {the a will add a slider, which you can play around with, a=1 is the best fit}, 2) y=-1/(1+cos x) +2 & 3) x^2/(π/2)^2 +(y-1)^2/(1/2)^2=1. Am I wrong? P.S. I tried to post a link to a screenshot I made but failed even after inserting spaces in the address...
this was insane watching this from india at night 3 o clock... loved the way how the series come out to be very beautiful just by using a basic integral...🥰🥰🥰
what i learnt is leaving kamaal with free time would be deadly since he plays with simple integral then transforms them into beast looking sum especially infinite sums😅
i think he just milks these results from already existing ones (which is a common way of obtaining new stuff by the way) he probably was playşng around with the original integral and asked “what if i series expand this and do this and that” at least this is how i think this one came about
Hi,
"ok, cool" : 0:49 , 1:32 , 5:48 , 8:34 , 9:56 , 12:11 ,
"terribly sorry about that" : 4:09 , 5:06 , 9:34 , 10:17 .
Terribly sorry about that😅
5:48 was actually okay cool
@@wassimaabiyda Oh my bad, thanks, it's fixed.
This is the integral of quarter of an ellipse!!
YES IT IS!
(why am I yelling?)
@@maths_505
I am not convinced. It comes close but it is not an ellipse. It has pointed edges. I tried it on Desmos. You can try for yourself too. I entered the following equations for comparison:
1) y=1/(1+acosx) {the a will add a slider, which you can play around with, a=1 is the best fit},
2) y=-1/(1+cos x) +2 &
3) x^2/(π/2)^2 +(y-1)^2/(1/2)^2=1.
Am I wrong?
P.S. I tried to post a link to a screenshot I made but failed even after inserting spaces in the address...
The Weierstrass substitution is remarkably powerful. Thanks for showcasing it in this video.
I got spoiled by your "ok cool".😅
this was insane watching this from india at night 3 o clock...
loved the way how the series come out to be very beautiful just by using a basic integral...🥰🥰🥰
bro had to give us another phi jumpscare at the end
This opens up the door to a whole nation of infinite series
Beautiful result , thanks for making this video
Very nice result. Thank you.
Please continue these kinds of videos where u play with these kinds of integrals which results in cool infinite series
i will always watch it 😊
this result can be used to get the maclaurin series for arcsin(x), and for arcsin(x)^2. They turn out to be basically the same interestingly enough.
And here I was using the duplication formula, splitting up the sum into even and odd indices and being absolutely perplexed
this is amazing.
you really had to blueball us till the end
The cherry on top of the cake comes at last.
I had to compute the fourier series of this one. Hardest integral I've ever solved by myself
What if you used conyour onwtgration instead?
Does this imply that pi is emergent from the golden ratio?
keep up
what i learnt is leaving kamaal with free time would be deadly since he plays with simple integral then transforms them into beast looking sum especially infinite sums😅
that's absolutely insane, how do you think about those??? i mean, all this came from a really basic integral, w o w
i think he just milks these results from already existing ones (which is a common way of obtaining new stuff by the way) he probably was playşng around with the original integral and asked “what if i series expand this and do this and that” at least this is how i think this one came about
That's exactly how this result came about
بهت خوبصورت!
cant you simplify 3-phi? 3-phi=2-1/phi=(2phi-1)/phi=sqrt(5)/phi, so the radical simplifies to sqrt(pi*phi/sqrt(5))
If we put x=0 does that sum evaluate to 2/√π ?
In the limiting case yes
Oh god wtf is that series
Upload 2 videos everyday
ye i think sometimes he needs to sleep
@@Jalina69 sometimes😂
I=4√πΣ(-φ)^kΓ(k)/(Γ(k/2))^2...poi????..=4√πΣ(-φ)^k/β(k/2,k/2)...
Second
Most of our indians wont do this types of problems