Solve This Tricky Integral to get Free Wi-Fi!
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- Опубліковано 23 гру 2023
- Have you ever had to solve a mathematics problem to gain access to Wi-Fi? Let's see what it involves!
Apologies for the poor audio quality in this video, my microphone broke and I had to use the default audio from my camera which echos quite badly!
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For those of you that are new here, hi there 🌞 my name is Ellie and I'm a Cambridge Part III Mathematics Graduate and current Astrodynamics Software Engineer! This channel is where I nerd out about maths, physics, space and coding so if that sounds like something you're interested in, click the subscribe button to follow along ☺️
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⚠️ For anyone wondering why the integral was only half of the semi-circle - it’s due to the square root in the integral. Because of the square root, y cannot be negative! I should really have removed the bottom half of the semi-circle but I thought it was clear once I explained that we only needed the top half. Hope that clears up any questions!
Yeah, that got me. Thanks for explaining it
Answer was 2π
U Made mistake at calculating the area of semicircle
You solving integrals are satisfying me, and i want to know more about them :O
@@gsrarmy3616the area of the semicircle is 2π, you’re forgetting the factor of ½ that was already on front of the integral
You have to appreciate that there was no crazy integration technique involved, just pure mathematical reasoning. Understand the problem and use logical reasonings to get to the result. This is what a mathematician does! 10/10
The integretion with the circle got me , wow I thought Ellie was gonna use the trig substitution but wow , that was some gmreally good reasoning , thank you so much !!! I really liked this exercise and your explonation keep it up !!
The engineer in me went: "Oh, it’s one of those edgy problems? Is the solution pi?"
Because requiring 10 or 5 digits means the solution has to have that many digits as well and nothing in the equation suggested division by 7 or 9 or the like, that result in those kinds of fractions.
Then it’s edgy and the problem is probably about the equation and not the answer being complex.
@@PH4RXlol same
@@PH4RXwdym “edgy”?
@@ayuballena8217 To begin with, it's probably just a gag sticker for the maths lab, etc. and not a real password.
It's like a Facebook post with "only 3 people in the world could solve this!1!" (it's not that bad but I hope you get my point): it's an equation with a simple solution crafted to look complex and scare off people with low maths skills.
I love that you used the semi circle, it brought back a long lost memory from Calc AB before I learned trig substitution. Great video!
I appreciate just how knowledgeable and cohesive you are to be able to hand guide me through this. takes a lot to simplify haha
Thank you so much Ellie. You are amazing! You break down complex problems into small-sized pieces that anyone can understand. Thanks for sharing your gift and for taking the time to do this. It takes a lot of effort and work to make these types of videos. THANK YOU. You are now my top UA-cam channel. Keep up the amazing work! Thank you again.
Top tier solving. Process explained beautifully. Earned a sub.
loved your way of explaining, its simple jet effective.
I’m surprised of how understandable this was, considering I never did integration. Good job Ellie, In particular I liked the speed of your video. It made it easier to understand your steps.
"Truly impressed by the way you used mathematical proofs to solve the integration question! Your logical approach and clear presentation made it easy to follow along. I particularly liked everything you did. Keep up the excellent work! Would love to learn more about your techniques"
I appreciate it for the effort you put on this, explained it so perfectly!
Hey ellie I'm new to you're channel. Nice to meet you. I love mathematics. You're explanation is great. I'll go through you're other math videos and will look forward to more math videos from you :)
Thanks sister now I can learn maths from you with free Wi-Fi 😊
I love it so much , please continue
Even though not a maths student, I still watch your videos and I Love your accent, it's really very sweet🧡
Very nice perfformance Ellie
Great sweater. Merry Christmas!
You know i saw X^3 multipled by cos and i screamed 0, Then I started to do a trig sub in my head, and you showed me a new simpflication i never though of. Great stuff.
Still impressive of calculus 2 knowledge level. I am still self study calc 2 and it seems complex. Glad you solved it and good luck in your goal.
with several prerequisites of functions, elementary algebra, geometry, to my surprise I was able to get the calculation, not just the ease of depth, but the instructor has rare quality of common reasoning, no BS, and a kind honest heart to not make things muddled to make themselves look good
Smart approach.
When I was going to the 9th grade, I was looking forward to learning these things, but I just learned them this year and I love pure mathematics.❤
Thank you Ellie
this was really elegant. wow
This was a beautiful solution to the Free WiFi problem. I enjoyed watching this video a lot.
Loved this video. ❤🎉
Took me most of the video to see the design of the jumper😂. Great video rolling back my undergraduate days !!
Excellent explanation. I wish you were my teacher 👍
Taking area of circle is a great idea
I am currently starting year 11 maths and this stuff has always seemed super hard to learn but you taught it well so that even I can understand thank you also wondering how hard this question is compared to other
Thank you for the video.
You explained the odd and even function better than my math teacher could in a whole semester I appreciate but feel sad for my teacher being horrible at his job 🙃
You simplified the second integral to a primary school formula.😊 As a beginner I evaluate the second integral which led to an arcsin function. After I substituted the boundaries of the integral, it gave me the same result you got but I spent on it a plenty of time😢
You are legend solving integral with using integral legend hats off 🥳🥳
For some reason I remember that this was the first integral I was ever exposed to even before taking a calculus class. It doesn’t require very hard integration techniques and just requires logic.
Thank you very much My teacher ❤
That I2 looks simple but the way you solved is pure integral mathematics.
Thanks professor 😊😊😊😊
Great teacher
Great video! Thank you!
Very informative videos
Great video but I really wondered what your approach had been to solve that integral of the semicircle. Obviously with these boundaries your approach was by far the simplest, but could you maybe show with which technique you would approach such an integral? I study medicine but find a lot of joy in doing math, so that would be awesome! I came across that sort of integrals a lot whilst practicing the length of a curve by using integration of line segments…
Nice. Thank you.
great video👍
Good work ellie mam .
Very briefly explained. I left BSc Math in 2004, but today i gone through such integral solution (by chance) and had tears in my eyes, how we used to solve these equations without any guidance and lack of solution materials notes etc, but internet has made it worldwide source of guidance. Your graphical representation very helpful for solution of such equations.
(From Pakistan)
Very unique explaination ,
Nice lernt now thing on how to use analysis and logic Thnk u
Well done
Thought this would be a really tough one. But, surprisingly it's too easy.
Awesome!!!
Thank you very much, now I can steal the neighbor's Wi-Fi here with peace of mind. It's brilliant to use the concept of parity to cancel or simplify the integral, I use it a lot in electromagnetism, but I confess I wouldn't know how to solve this integral without you.
UR explaining complex MATH problems simple)
With the dx inside one can interpret it as fractional derivative. And the answer is (-4/(3Pi))*(8^(1/2)-1) in that case.
omg Ellie you make me fall love every day! you make math so fun for me.😆
Excellent❤
your hand writing is too beautiful for you to be a mathematician! I also loved the explanation of the second half of the integral
aaah thank you! 🥺
Wtfdym "to be a mathematician" 😭😭😭😭😭💀🙏🙏🙏
@EllieSleightholm Thanks for sharing Ellie. I really hope you can respond to my other comment whenever you can. Happy Holidays
@@PhalitSehgal with my limited experience of just high school math i notice we never write so neatly ever. "mathematicians are lazy" as one of my teachers said, we just wanna get to the end haha
So, should we be less demanding about the handwriting of a mathematics teacher when compared to the other teachers? Why?
Talk about biomathematics. I want to complete a master's degree in it, but I am hesitant between it and industrial mathematics
Your clarity and detail of explanation is really good! Very well explained. Something many mathematicians are not good at doing.
Thanks a lot. Now I can log in to the wifi.
hi ellie, can you create math formula for storage any number then recall that number also with math formula? your videos was awesome. i subscribed 😊🎉❤
can you try and solve some math olympiad questions ? I do them myself and they're so fun to do and watch
Yes!! I’ve been planning a few 😁
I was a little confused as to why the area is only the top part, but its simply because the square root function means only the positive part of the function for anyone else wondering.
Ah yes, sorry i missed the explanation of that out! I’ll add a pinned comment for anyone else wondering ☺️
Both can be considered
y^2+x^2=r^2, x^2-r^2=y^2, y=±(x^2-r^2), so the positive bit is above the x axis
That's a great way to solve it
fun fact: if you have to solve an integral for wifi password, the answer is either pi or e. trust me
Although I don't understand anything, but these are beautiful
After 1st step we can just use kings property in first and in the second one we can put x as 2 sin theta
I’m glad I stumbled upon your channel-the content is interesting and well presented! One of my favorite biographies is “The Life Of James Clerk Maxwell”, and I particularly enjoyed the chapters on his time at Cambridge, so it’s interesting to see the sort of modern version of the tripos experience. One thing I’m curious about is, when approaching the problems in your videos, do you find you are able to do them without looking up any hints or answers? Granted, a Wi-Fi password question may be intended to be a bit of a fun softball question, but some of the other problems you’ve tackled are far more nuanced; I’m mainly curious if a masters in mathematics at Cambridge requires one to be at such a level that those sort of problems can be tackled impromptu.
who is the author who wrote the maxwell biography you read?
@@Leloup7 It was written by a friend of Maxwell, Lewis Campbell (and William Garnett). It’s quite an old book now, and is likely public domain, but I picked up a physical reprint on Amazon.
The smartest brain I have ever seen ..❤
I appreciate you
I hope you will guide us, I am interested in Physics and Maths, so which should I do Masters in?
you are so great
Looking at it quickly.
I := [-2,2] is an interval that’s symmetric around 0.
So integrals of odd functions [f(x)=-f(-x)] over I will evaluate to zero.
Call the result of the integral Q.
Q = integral over [-2,2] of q(x)dx,
where q:=(x^3*cos(x/2)+1/2)*sqrt(4-x^2).
q=(u*v+1/2)*w, where
u(x):=x^3 is odd.
v(x):=cos(x/2) is even.
1/2 is even.
w(x):=sqrt(4-x^2) is even.
for functions
[even] * [even] = [even].
[odd] * [even] = [odd].
[odd] * [odd] = [even].
u*v*w is odd. - it cancels under the integral.
(1/2)*w is even. - it remains.
Q = integral over [-2,2] of (1/2)sqrt(4-x^2)dx.
Quick change of variables {x=2s, dx=2ds} gives
Q = 2*Integral over [-1,1] of sqrt(1-s^2)ds.
The integral is the area of the half unit circle. Twice that is the area of the unit circle.
Some might know it as π.
Because of your this video, I could get a mcq correct in my exam today
I love you thank you
Optical Illusion in your sweater 😮
Tank you so much
Cool vid
Thanks PROF UR simply unthinkble.
I saw this meme when i was like 11, obviously i had 0 clue what integration was, now I'm 17, preparing for jee, and even tho the question does look scary i considered giving it a try, and the question did trickle down after applying king's lol. Refreshing and nostalgic
elegant 👍
Merci pour le partage.
Nice video
woah she's really good at match yoo
the way i called it being pi from the beginning
This is really funny that instead of giving free wifi, they ask the people to seek to get wifi to solve an integral
I just use Matlab Symbolic solver; that way the answer is quick, never any errors and my head doesn't hurt...
In Portugal x^2+y^2=r^2 isnt a circle but a circumference. To be a circle it has to be it has to be x^2+y^2
Where did you get your sweater?
hp-prime spits out the answer ‘not quite π’.
Beautiful explanation, your follower is an Iraqi Arab
try to solve any JEE ADVANCE questions
can u make a video on doing a STEP paper
Yes!!
Beautifully explained. I'm in my 60's and not done any calculus since my early 20's. Great to have something explained without me losing the plot in less than a minute.
Good way
I definitely would have used trig substitution without thinking. Good catch about the half circle. Definitely an easier way than trig sub.
Can you make a vedio on cube root of unity
I spotted the odd part straight away and realised the integral was the the area of a quadrant of a circle of radius 2. It would have been better if the password was the LAST 10 digits of the answer though.
Do you add constant at the end of answer??
JEE adv aspirant and i got it right LETS GOOOOO
Pi by inspection. Odd part vanishes. Rest is 1/4 the area of a circle of radius 2 = pi.
I clearly understand mam