Area & Arc Length of a Cycloid (one arch)
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- čas přidán 13. 09. 2024
- Check out this video for 100 integrals so you won't forget your integrals again! • 100 integrals (world r...
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Area of a cycloid, 1:00
Arc Length of a Cycloid, 8:45
Parametric Equations Overview: • Parametric Vs. Cartesian
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Comfy bprp maths after a long day of work is best maths
0:45 The arc length and area can be calculated by using y = 2r(arccos(x/r) + sqrt(1-(x/r)^2)) and integrating between -r and r. It's not exactly what you asked for, but it will give the correct answer. The difference is that the circle is rolling on the y axis instead of the x (along with a few simplifications to the equation). I also don't know how hard that is to integrate.
I prefer the first integral. I'm not a math student, I'm just an agronomist, but I love your videos. Please keep going! Greetings from Italy!
Thanks!!!
10:44 the true fans watch the whole video :)
Thank you!!!
Darn. No π in the arc length.
I know right!
Seriously, what the heck?!
It's unsettling
thats literary why i was here watching this video
I love your enthusiasm! Thanks for working this out very clearly.
10:43 hahah, thank you for being an awesome tutor. I like watching your explanations because they're clear and you remind me that math should be fun! It's hard to remember to enjoy learning when exam season comes around, so thank you for all your videos and your help :)
10:43 love you bprp
Thank you!!
The cycloid passes the vertical line test, so it is actually theoretically the graph of some function f. I was thinking that you could come up with a closed form of f(x) for the first arch by defining a function g on the interval [0, 2pi). Then you could define f as f(x) = g(x mod 2pi).
I remember doing this and the rotation volume of a cycloid for high school, so cool. Nice vid
The area is 3 times the area of the circumference with r radius.
this question was in my book so awesome
1+1 = 2 - you've got to say it with *authority*. I never have been told before in my life with such enthusiasm that 1+1 = 2.
10:43 Watching the whole video. Awesome curve. Mind-blowing properties.
Why do you make this sound so exciting ! Lol I am having a hard time, but your videos are so encouraging! Thank you!!
Well, this went WAY over my head but still interesting to watch 😂
Although I didn't take calculus in high school, I still like your videos.
They are so satisfying to watch. 10:45
Crazy result of 8r !!! Thanks
Oh thanku
I have a presentation about cycliod,u help me alot❤
Your right hand on the thumbnail looks like a zot zot zot symbol 😄
Dr Peyam
It’s the right hand and the left hand rules!!!
Hahaha, makes sense!!! Zot zot zot!
10:44 Still watching. I’m gunna have to stop so I still have time to do my precalc HW. Looking forward to tomorrow’s video though!
Thank you!!!!
At first glance the integral for the arc length looked more difficult. The area integral was simple if you knew the identity. Then again you make everything look easy hahaha
Pretty good video. Thank you for your beautiful job. Keep it up.
my savior thankk you
can you give me the name of a book who content like these problems , thanks , i love your videos i watch you every day
First thing first . . . There was no mention whatsoever on HOW the parametric equation of the cycloid was derived.
And by the way there indeed IS a Cartesian way of writing the equation (without using parameters).
Thus the equation of the cycloid as the locus of a point on the circumference of a circle radius r rolling on the x-axis, beginning from the origin, is given by . . .
x = arccos(1 - y/r)) - sqrt[y(2r - y)]
Wow, I would have predicted the arc length formula to include π.
Can you use disk method here?
10:46. True fan
Just checked - 1+1 IS 2!
Respect your AUTHORITAY!
13:05
Your problem works out to be almost the same as my homework problem (just without a constant "r") and I'm stuck on the (2-2cost) in the sq.rt so I'm hoping you're about to show me how to make it easy lol
10:42, I'm still watching! I think this step will be a little harder
Very cool, but can you do the integral of x^(dx)+1 ?
Yea, Dr. Peyam did a video on that already: czcams.com/video/shdK9DAiDBE/video.html
In these times of coronavirus you have officially become my tutor/professor 🤣
Cartesian equation of the cycloid
x = r arccos(1 - y/r) - √[y(2r - y)]
10:44 watching from the very start as always!
GREAT WORK....
Old time friend 1+1=2 need to say with authority!
Ha ha ha, he did the same thing with the '2 * -2 = 4' at 18:44. I guess he likes his constants.
Yes I love the confidence! You really helped a lot! Also the jokes
It does not matter here since, for t going from 0 to 2pi, t/2 is going from 0 to pi and so sin(t/2) is always positive. But in a general case, when you put the sin square out of the square root, don't you have to take the absolute value ? (sorry for my bad english)
Sin^2(t)=(1-cos(2t))/2
high standart content given by red pen black pen. very impressive sir. i found it usefull for my deriviations. CAN U ALSO PUT A VIDEO ON BRACHISTOCHRONES? ( a big fan from india) well one doubt how were u able to use two pen in one hand? ur amazing sir!!!!!!!!!!!!!!!!!!!!
thank you
you need to explain how you got the area formula
Can you show how to find value of sigma of 1/(n^n) which n from zero to infinity please!!!
When I’m setting up the integral for the arc length: I work out the expression for the inside of the square root first: then square root it
blackpenredpen always has interesting problems in his videos.
Laurelindo thank you!!
maybe you can do a video on the logic behind the sum and difference trigonometric formulas
MR blackpenredpen
I have challenge for you which i failed to do it ,the challenge is
the length between two point on the Ellipsoid by using any coordinating system .
There’s an integral in this video so I sure this is relevant enough (maybe...)
How would one integrate (the indefinite integral of):
(cos(2x)-1) / x^2
(I might just be an idiot box)
That almost looked like Dirichlet Integral.
(1-cos(2x))=2sin²x
So if you make the trigonometric substitution, then you just get
−2∫(sin²x/x²)
I don’t know if it has a closed form but if it’s from -∞ to ∞ then you can indeed solve it.
10:44 hmm.. I watch all your content, but am I a true fan even though I haven't done calc since first year uni over 10 years ago? Lol hope so! Love your videos! :D
Sir plz make video on iit jee problem
Well I found it. y = r(1-cos (butch(e/r))), where e =x and butch(x) is inverse function of f(x) = t-sin t
Why do you have to add the x'(t) in the integral?
You know at 10:00 I thought that you showed your true colours but it was near 10:50 actually .
As for integrals as long as you know the correct method they are easy , like practicing a spooky voice.
NICE!
Really should have pointed out that the answer is the modulus of cos(t/2) but that in the range 0 - 2 pi that this is just cos(t/2)
Now let's see what happens if we roll a circle with radius R (not necessarily the original r) on top of a Cycloid, let's see how long will the arch be.
We will get an "epicycloid"
en.wikipedia.org/wiki/Epicycloid
@@blackpenredpen that is very epic
@@gergodenes6360 And if you build it from a cheese wheel, it's a fol épi cycloid.
How would you calculate the radius of the circle if the point is 64pi cm appart? :(
Amazing!
10:45. I think its more difficult but I feel like I have seen it before....
Tks BRO Brazil love U
Sir, how to show that a cycloid is periodic?
Surface area would just be integrating the area multiplied by the y value, so since y = r-rcost, multiplying gives r int(sqrt(2-2cos)*(r-rcos) )dt, which equals sqrt(r) * integral(y^(3/2) dt). using the same double angle formula gives sqrt(r) * 4 * integral(sin^3 (t/2))dt. I guess let u = t/2 real quick to get sqrt(2) * 8 * integral(sin^3 (u))du, and then do that integral that I forgot how to do.
oh oops that last sqrt(2) should be sqrt(r)
I love your videos man. Why sqrt sin^2(t/2) isn't |sin(t/2)|? Also 10:40
I belive it is because sin(t/2) is always positive between 0 and 2π
Hi, i love this channel, hey, i need your help with this secuence
{tan(2/n)/sin(n/2)}, i from Costa Rica, nice to meet you. The question is if converge or diverge.
It all went through out my head because I am a student. But I clicked video to increase views and liked it.😂😂😂
Is an isosceles triangle with a sum of interior angles of 3π a circle?
Can you apply a similar approach to calculate the area and length of an ellipse?
If I recall correctly, the arc length is an integral that you can only do numerically. No need to recall; you can look this up.
Epic.
I'm sorry, what is your profile pic from. I keep seeing it everywhere
@@benjaminbrady2385 deus ex
10:46 hehe, true fan hehe. Well I don't know why ur doing that right now, but I'm still having fun at maths so I watch you xD Most I do understand. (Pupil 11th grade) xD
Supposed to be studying for my AP Calculus exam but somehow I ended up here 😂
17:36 no absolute value because sin(t/2) >= 0 for t in [0, 2 pi]
Pefect
10:50 - I'm a true fence!⸮
1+1=2 and 2*2=4 yes ! that was difficult
Can you do a video on solids of revolution for rotation about a slant axis (such as y=x)?
Better to wait for linear algebra coordinate transformations.
findning area is easier(maybe because i didnt know the formula of arc length:))
Pleas slve this
The integral of (x^5+1)^10,
I don't want to spend my life multilpying something to the power of 10
is there anyway easier .?
There’s no other easier way to do this. You would have to multiply it out and using the Pascal’s triangle and then do the integration.
Use binomial theorem. Sum{k=0 to 10} 10!/(k!(10-k)!) (x^5)^k. The integral is Sum{k=0 to 10} 10!/(k!(10-k)!(5k+1)) x^(5k+1). Just evaluate each coefficient to get answer. Don't forget + constant.
Cant you apply the reverse of the chain rule here.
hi, can u help me with an integral, ((1+sen^2 x)/(1-cosx)^2)dx
16:21
Minus 1, that's 3. #QuickMaths
Love your videos bro, is there any way I can get in contact with you...??? Do you offer personal tutoring services??
What do you think
and it is too interesting that the result of arc length is a rational number, and don't include pi , any explanation ?
10:47 im a true fan
Arclength formula seems more familiar.
3:37 lol
2nd part is much harder at 10:32
I was somewhat surprised that the shape is neither an ellipse nor a circle arc, but a 'cycloid' and not a conic... - hmmm - interesting
I didn't get the point of 2 pi
great
i'll meet you outside, Calculus.
10:44 harder cuz of the square root
I’m guessing
10:40 i'm a real one
Yay finally cycloids, ellipses next?lol
4Head
Make videos on *JEE Advanced* _Mathematics_ Your subscribers will be more than _T-Series/PewDiePie_ 😉
10:44 watch the whole thing or you won't understand a thing
thanks!!
he used blue pen ???
Unexpected fr