Hey bprp. I've noticed that you seem more on edge towards negative comments lately. I hope that you're alright... more negative comments is a natural result of growth and most people aren't actually expressing hate but are often memeing or making an obscure reference. Remember, anyone who comments on more than one video is here because they love your videos, not because they hate them 1000000/1-x
I'd just like to say thank you for your help though these videos, particularly on integration. I've been studying the topic on my own ahead of my lessons, and these videos are an awesome way to put the theory into practice and better comprehend what it's all about.
Thank you for the education! Your videos were my motivation to foray into calculus and finally got me back into learning math on my own (doing math for fun lol) keep it up! :)
You can certainly write the sequence of areas as a function of n by using the bounds you've provided and I believe that you get 1/12 * pi^3 *(3n^2+3n+1)-pi/8. There may be some recursion you can develop from this, but I don't have any ideas off the top of my head. At least this allows you to provide the area of any loop that you want!
Thank you blackpenredpen for another amazing video. This will definitely help me out for the AP Calculus BC Test. Also could you please make a video on differentiating a polar function?
How can you write cartesian y=sin(x) in polar coordinates and then integrate the area? It in some sense has no area at all... but if plug to this equation it would give area, right? (Because curve isn't "closed"). This case in cartesian case it gives 0 area if n*2*pi integration range is used. This case same in polar could give area of circle with radius r=n*2*pi..(???)
I found this document on the subject; the first page is a proof, the rest showing how to use it (in table form): ramanujan.math.trinity.edu/rdaileda/teach/s18/m3357/parts.pdf
is it possible to compute when the area of a circular segment has the same area as a square with the same side length of the circles radius? I came to x-sinx=2. I don't see any way of getting any more out of this, but you might.
Here’s an interesting question: how does one determine and prove mathematically whether or not the whole region 0 to 2π is similar to the region 0 to π?
Gabriel Taylor Hmmm very interesting! My first thought is to compare how their arc length and area changes. But it’s just a quick thought. I wonder if anyone else has any other idea?
@@pierreabbat6157 Is that really true? For small angles, sinx=x, so x.sinx = x^2 --> finite curvature at 0. There shouldn't be any discontinuities anywhere since it can be differentiated as many times as you like. Another way to think about it is that the derivative of x.sinx will be x.cosx+sinx, which is clearly finite at x=0 (and all finite values of x). That also allows you to see that the gradient at the origin-crossings will change with a very interesting pattern -- 0, -pi, 2pi, -3pi, 4pi, etc.
Joseph Hughes This is called the DI method. D stands for differentiation and I stands for integration. He is setting up the tabular method to show a quick way of doing this.
Hey bprp. I've noticed that you seem more on edge towards negative comments lately. I hope that you're alright... more negative comments is a natural result of growth and most people aren't actually expressing hate but are often memeing or making an obscure reference. Remember, anyone who comments on more than one video is here because they love your videos, not because they hate them
1000000/1-x
Thank you Ben.
can someone please explain me that *100/1-x* thing
@@hamiltonianpathondodecahed5236 1/1-x is the "Best friend" powerseries so by multiplying it, you're saying very best friend or best friends
Benjamin Brady yes! : )))
Black pen red pen blue pen?! 🤯
Brain Gainz haha I saw that!! 😂😂
Hahaha
@Chanelle L Thanks!!
the way you smile while explaining makes me happy and shows how much you enjoy keep up
Thanks, will do!
"It's not because I cannot draw, but because it's not a circle."
Since when were those two things mutually exclusive, huh? ;)
Art is not in painting, but in math, bprp! We do know your drawing was great.
Awww thank you!!!!
i like that you always simplyfy after writing it down. there is never a step lost
S1nwar thanks
You draw an amazing not-circle! It looks spot-on!
I don't believe I have ever seen integration by parts done that way... mind blown.
It's called the "tabular method for repeated integrals"! Very useful for trigonometric functions and e^x (:
"uploaded 36 seconds ago"
"First comment 7 hours ago"
Excuse me wot?
Polar time coordinates
Patrons get early access
I'd just like to say thank you for your help though these videos, particularly on integration. I've been studying the topic on my own ahead of my lessons, and these videos are an awesome way to put the theory into practice and better comprehend what it's all about.
Kostas T. My pleasure!!
I got an A in Calc II this semester because of your integration videos. Thanks for your help.
Wow this is actually really interesting :) Fantastic video!
Joecake Gamedev thank you!
Yaaaay! You’re the best!
Dr Peyam thank you!! Btw, does your calc class cover this?
blackpenredpen Sadly not 😣 We do polar coordinates, but not calculus with polar coordinates 😭
Dr Peyam oh
wow, perfect timing. Learning about polar area right now so thank you!
Michi Plays I have more examples. You can check my playlist. : )
Haz un álbum de puros problemas de cálculo vectorial.
Hello l'm Korea student your math is great useful
Thank u blackpenredpenbluepen
: )
bro 7 hours how
@@eansengchang6840 I was wondering that too...but how🤔
Sergio H it was released on my Twitter first last night.
Just what I was looking for!
Can you do something about Diophantine equations?
Find all the parametric solutions for (x,y,z)^3 = 31.
Very good review for calc 2...thnx bprp 😀
Thanks!
You use colours of pens very nicely
DI table caught me off-guard lol! Maybe I need to study or watch some videos to understand it more...
Explain about sketching a polar and parametric curves.
So good!
J.J. Shank thank you!!
Thank you!
Thank you for the education! Your videos were my motivation to foray into calculus and finally got me back into learning math on my own (doing math for fun lol) keep it up! :)
Great video. I am now interested in the sequence of areas of each loop.
Hmm, it would be from n*pi to (n+1)pi and I wonder how the values will go.
You can certainly write the sequence of areas as a function of n by using the bounds you've provided and I believe that you get
1/12 * pi^3 *(3n^2+3n+1)-pi/8. There may be some recursion you can develop from this, but I don't have any ideas off the top of my head. At least this allows you to provide the area of any loop that you want!
I don’t know what is going on in the universe but every time he posts it is somehow the same thing I’m going over the exact same time
Because I know the secret! : )
And I bet sequence and series are coming?
he might be your student
If the inner loop goes from 0 to π, then the outer loop goes from π to 2π.
The area inside the outer polar curve and outside the inner curve should be 1/2π^3 if I did my calculations correctly.
Thank you blackpenredpen for another amazing video. This will definitely help me out for the AP Calculus BC Test. Also could you please make a video on differentiating a polar function?
I have a playlist in the description. : )
The larger circle area should be 7/12π^3-1/8π
How can you write cartesian y=sin(x) in polar coordinates and then integrate the area?
It in some sense has no area at all... but if plug to this equation it would give area, right? (Because curve isn't "closed"). This case in cartesian case it gives 0 area if n*2*pi integration range is used. This case same in polar could give area of circle with radius r=n*2*pi..(???)
I wish I knew what is that D I table you always draw when you do integration by parts
I found this document on the subject; the first page is a proof, the rest showing how to use it (in table form):
ramanujan.math.trinity.edu/rdaileda/teach/s18/m3357/parts.pdf
Also, pretty salty that I didn't come across this until the final year of my PhD >_>
ua-cam.com/video/matDV3XL2J8/v-deo.html : )
is it possible to compute when the area of a circular segment has the same area as a square with the same side length of the circles radius? I came to x-sinx=2. I don't see any way of getting any more out of this, but you might.
I think that the sign of the middle blue is not minus but plus(+½θ·sinθ = +(½)(¼)(π)=π∕8).
Could You prove the integral form of area between curves in polar cordinates, please?
Here's an example: ua-cam.com/video/JxIJLzDp-L4/v-deo.html
Again, the formula is just "the area of the sector"
I will do the proof one day.
Here’s an interesting question: how does one determine and prove mathematically whether or not the whole region 0 to 2π is similar to the region 0 to π?
Gabriel Taylor
Hmmm very interesting! My first thought is to compare how their arc length and area changes. But it’s just a quick thought. I wonder if anyone else has any other idea?
It's obviously not, since the graph has a cusp at θ=0, but at θ=π it passes through the origin with finite curvature.
@@pierreabbat6157 Is that really true? For small angles, sinx=x, so x.sinx = x^2 --> finite curvature at 0. There shouldn't be any discontinuities anywhere since it can be differentiated as many times as you like.
Another way to think about it is that the derivative of x.sinx will be x.cosx+sinx, which is clearly finite at x=0 (and all finite values of x). That also allows you to see that the gradient at the origin-crossings will change with a very interesting pattern -- 0, -pi, 2pi, -3pi, 4pi, etc.
Actually, now I see that I goofed. Polar form. Duh. Ignore me.
No „rad“ included. Like it.
Hi, blackpenredpen! What university did you graduate from?
All of. Them
@@BlokenArrow - LOL
If it Area of the bigger circle looking thing, would it be \theta replaced by 2\theta?
Start a linear alegra series
Sign error: (I don’t have theta so using @) -2@ times -1/4 cos (2@) = 1/2 @cos(2@)
Theres a negative outside too
What is that method of IBP?
Joseph Hughes This is called the DI method. D stands for differentiation and I stands for integration. He is setting up the tabular method to show a quick way of doing this.
is abs implicitly assumed there? sin(x) is negative for x=pi...2pi, so it is incorrect polar coordinates equation
No, r is allowed to be negative; it just puts the curve on the other side. That's why the second loop is also on top, despite the angle pointing down.
In my calculator, I plug in the integral and I get 2.19, is this correct?
Lora Howsian
Hmmm try to enter what I got on the board to see if they match.
blackpenredpen I did, I got approximately 2.19, and i subtracted the result you got and I got 2.19 too.
Can you do a video talking about and introducing polar coordinates :) #yay
I will put them in the description!
@@blackpenredpen thank you! how about a video talking about polar curves vs rectangular curves?
これも普通に積分しちゃっていいのね
あれ、なんでそうなるんだっけ
基礎的な事が抜け落ちてるなあ
blackpenredpen
#yaaaay
Good pa
so easy...
WHY DID YOU UNFOLLOW PAPA FLAMMY ON TWITTER?
?
Arya kills the night king.
I am going to hell for this spoiler.
Does anybody know that the special theory of relativity is completely stupid theory that contradicts logic?
Сергей Мишин,
No, I didn‘t.
Make a video.
@DY_Physics If they (Maxwell's equations) contradicts logic then they are fake. Is it right, isn't it?