How to change the order of the differentials of a triple integral? Animation and the rest of the answer by Fematika, • Changing the Order of ... , For more calculus tutorials, please see @bprpcalculusbasics
Пікірлер: 123
@blackpenredpen6 жыл бұрын
For the rest of the answer, including animations, see kzbin.info/www/bejne/hmq9d2amj6-sodE
@atulit6 жыл бұрын
blackpenredpen graph of y = x^2 is wrong
@yaleng45976 жыл бұрын
can you please do the derivative of functions invovling lxl ? (such as lxl, sqrt(lxl) lx±2l, l3xl and lx/7l etc.) because i am bad at differentiating functions which invovle lxl.
@wkingston12486 жыл бұрын
Moral of the story, hire art majors to help draw 3 dimensional graphs because that's the hardest part of the solution.
@ScholarStream_254 жыл бұрын
😂 I swear bro
@divisix0244 жыл бұрын
Me and my classmates in calculus admiring the professor’s hand drawn graphs...
@felikavalencia19334 жыл бұрын
@@divisix024 while my prof is just shitting and didnt even draw anything!
@D00000T Жыл бұрын
or build it in minecraft like one of my classmates once did
@bahuliyamanyapu76645 ай бұрын
@@ScholarStream_25 haha
@duncanw99016 жыл бұрын
Loving the cal 3 content! I haven't even taken the class, but I understand the things due to your explanation. A well-earned subscription.
@blackpenredpen6 жыл бұрын
Thanks!!
@user-vm6qx2tu3j6 жыл бұрын
Same
@SpencerRemy3 жыл бұрын
I would pay any amount of extra tuition if I could get quality lessons like this from my professors.
@subodh3733 жыл бұрын
If you I can help
@ScholarStream_254 жыл бұрын
I have never changed the order of a triple integral , yet I did that for double integral. Now after watching the video it feels really easy for triple integral
@GreeeenT6 жыл бұрын
how do you always post things that are relevant to my classes. seriously, everytime I learn something new you post a video about it as if you're in my class haha
@hafizmasum96006 жыл бұрын
Upload more on triple integrals bro
@marcioamaral75116 жыл бұрын
I love the way that the integral signs are in different colors!
@bernfernandes43805 жыл бұрын
Amazing content! I feel much more confident for my exam. Thanks x
@stephanm.tjaden38875 жыл бұрын
This was very helpful! Thank you.
@blackpenredpen5 жыл бұрын
Glad to hear!! : )
@p1eboi8043 жыл бұрын
Thank goodness people like you exist
@marinamaged962 Жыл бұрын
why do they make us do this
@fasebingterfe6354 Жыл бұрын
Majoring in math is the most hardcore way to learn how to draw that I've ever seen
@mikemichalarias80132 жыл бұрын
My man taught me math and then flexed a toblerone on me. I feel ashamed and greatful. Thank u.
@user-ms9sh2ed5v6 жыл бұрын
Three times two times one that's six quick maths
@MrCigarro506 жыл бұрын
Thank you very very much. This type of tool is much more common than one thinks.
@sajalgorai25704 жыл бұрын
wow... love from india
@user-gp6ms5mi2y6 жыл бұрын
Great work, Bprp, you have a great video up again.
@Prxwler3 жыл бұрын
Great explanation! I could understand it despite haven't even finished my calc 1 course lol
@malaygangwar5956 Жыл бұрын
Thank u sir u changed my life
@rybaplcaki72676 жыл бұрын
Please more multiverible calx!
@DawgFL4 жыл бұрын
If a question asks to solve a triple integral by changing the order in an appropriate way. How do I know which ones to change? For example if it is dxdydz, how do I know if I should change them all, or just 2 of them, etc?
@kylejohnson84473 жыл бұрын
Usially it is very hard or impossible to integrate in anyway besides the correct order in those problems
@AkashdeepSingh-qq5fw3 жыл бұрын
x = 1,-1 and this matches with ends of parabola bounds for dy but if something like x=5,-5 what will happen? does this mean that the integral is invalid because it does not make any sense?
@nullplan016 жыл бұрын
Oof, you can ask questions this late in the day... OK, so the outermost integral was in terms of z, which goes from 0 to 1 (we already had that). Now x... is going to be funny. Which values can x take in dependence only on z, such that any value for y inside our cheese-wedge exists? If z=0, then all x from -1 to 1 are possible, but the higher up we get the narrower that interval becomes. Until z = 1, when x = 0 is the only choice. What is causing the limitation? If z > 0 and x = -1, then y = x² = 1 would select a point with z > 1 - y. And we can't have that. So x can only be chosen such that x² < 1 - z. So we have our limits. x goes from -sqrt(1-z) to sqrt(1-z). Now we can pick y between x² and 1. So the final answer is z=0..1, x=-sqrt(1-z)..sqrt(1-z), and y=x²..1.
@andresxj16 жыл бұрын
nullplan01 Wow, that was amazing. I'm really looking forward to learning this stuff!
@briandutch74035 жыл бұрын
very helpful! Thank you
@user-eu5gl3th2t6 жыл бұрын
Thank you!!!! This is just what I needed
@user-eu5gl3th2t6 жыл бұрын
0:43
@blackpenredpen6 жыл бұрын
I tried to be like Gotenks
@user-eu5gl3th2t6 жыл бұрын
blackpenredpen LOL
@jadaayebae4 жыл бұрын
so helpful! and I love your smile!
@maymirror4 жыл бұрын
Your explanation is jst of next level🤘 ,u make things easier to get inside the head.
@nvapisces70119 ай бұрын
Me who can't draw to visualise: imma just use inequalities!
@retired55486 жыл бұрын
this should be called something like "Shuffling a pack of integrals"
@sajidrizvi46656 жыл бұрын
Wow You're so good at it. The way you explain is beautiful m
Please do an example where you have to find the bounds first
@BlurredLinez3 жыл бұрын
The Toblerone at the end lol
@davidbrisbane72062 жыл бұрын
I was able to visualise the triple integral volume using GeoGebra. However, I found that looking back along the x-axis, that this two dimensional view of the of the integral volume looks like a triangle bounded by the line z = 1 - y, x = 0 and y = 0. So, it doesn't quite match the shape blackpenredpen drew on the right of the board. I.e. no parabola shape sloping downwards.
@Koisheep6 жыл бұрын
Back in the day (two years ago) I was proficient at exchanging the dx, dy and dz, but right now I couldn't even begin. Kids, practice multiple integrals as well as 1D integrals
@nvidyyaa89193 жыл бұрын
Thanks for you video. You really save me for my midterm. xiexie
@silverwarrior11946 жыл бұрын
THANK YOU
@commissargamer Жыл бұрын
Watching at 2x before one night of exams!
@zacksbees3296 жыл бұрын
if only my math teacher could draw as well as you
@TuanTruong-dg7xq3 ай бұрын
thats crazy black pen
@HD-dw7zk4 жыл бұрын
thanks
@abofahad616 жыл бұрын
This is application for find the volume
@richardaversa71286 жыл бұрын
Only if f(x,y,z)=1. Otherwise a triple integral corresponds are finding a 4d "hypervolume".
@sergiokorochinsky496 жыл бұрын
Richard Aversa, the interpretation of the integral does not depend on f being = to 1 or different than 1. If f(x,y,z) is a density [g/cm^3], multiplying by dxdydz [cm^3] and integrating you obtain the total mass [g]. In the particular case of f=1, then the volume happens to have the same numerical value as the mass. If you want to calculate a 3D volume directly, you should simply integrate z(x,y)dxdy (all of them in cm).
@richardaversa71286 жыл бұрын
Sergio Korochinsky Good point, in the case of the function representing a density. My comment was in reference to the case of the function representing a surface. When the function represents a surface, the double integral gives the volume under the surface (and the triple integral gives a higher dimensional analog of volume associated with the surface). tutorial.math.lamar.edu/Classes/CalcIII/Area_Volume.aspx
@sergiokorochinsky496 жыл бұрын
The function does not represent a surface, the function IS a surface, and it represents a height. That's the reason z(x,y)dxdy has units of volume. Differentiating and integrating (from 0 to z), the double integral of z*dxdy becomes the triple integral of dxdydz, so... you were right! The number 1 is a special case. As soon as the integrand is different than 1, you are actually calculating a hypervolumen in 4D. ...Of course, you can continue doing the same with n variables, integrating all of them from 0 to 1, and obtain n-dimensional hypervolumes (all of them with the same numerical value)... so... I guess f(x,y,z)=1 is not so special after all. :-)
@kevincaotong6 жыл бұрын
Can you make a video on the surface integral please? I'm having a little trouble with it, especially since I learned it the parametric way on Khan Academy, and I'm not too sure with the non-parametric way.
@connormichalec10 ай бұрын
helpful
@mandeepubhi47446 жыл бұрын
Nice.
@Hussain-px3fc4 жыл бұрын
I saw a question about changing the order but I didn’t know why the limits of integration changed, even if the order was the same
@sanchitkumar73574 жыл бұрын
I am trying to calculate this problem where it says to calculate the Triple Integral ∫∫∫(3xy+2z^2) dV where the region R is given by $0
@snipergranola63594 жыл бұрын
Make videos on surface and itegral
@TNTErick2 жыл бұрын
0:42 Suddenly, ninjutsu.
@alyssagoins74853 жыл бұрын
Wouldn't it be easier to evaluate in cylindrical coordinates?
@fillername42233 жыл бұрын
Legend
@J.P.Nery.N.4 жыл бұрын
Good luck drawing this on a test lol
@SteamPunkLV6 жыл бұрын
when is your next stream going to be?
@davynrodocker893510 ай бұрын
What about dxdzdy?
@yaleng45976 жыл бұрын
Amazing video! Can you please do the derivative of functions invovling lxl ? (such as lxl, sqrt(lxl) lx±2l, l3xl and lx/7l etc.) Because i am bad at differentiating functions which invovle lxl. Btw, #Roadto100K d/dK=100 XD
@HaitaoWang2684 жыл бұрын
Triple integral. Yay!
@ram_20164 жыл бұрын
Tq sir
@iliasvrynas91893 жыл бұрын
but the z stops at 1-y WHY does the z-integral goes to 1?????
@user-el2pe5sh5v6 жыл бұрын
i have a question which is not related to the video. I want to make $100 and i make $1/hour. however, whenever I have$50, I will spend $50 to invest so that the rate of making money will double. as a result, no matter how many times I invest, the time I take to make $100 will never change. but, if I always spend $50 whenever i have $50, I can never make more than $50. it is a paradox. what is going on and can anyone answer me.
@theSASarethebest6 жыл бұрын
Do you teach calc 3 as well?
@xy79144 жыл бұрын
Is it 3D or 4D ? Because we have f(x,y,z) so actually we have w = f(x,y,z) so we have 4 variables ... Anyone can answer me ?
@abhiishekmuralidhar25654 жыл бұрын
Why wouldn’t the boundaries of y be from 0 to 1?
@drumman222 жыл бұрын
cuz it's in terms of dz
@siphilipe2 жыл бұрын
Any, even microscopic critic can be read?
@srpenguinbr6 жыл бұрын
I accidentaly worked out the problem for y going from x to 1 ;-;
@user-vm6qx2tu3j6 жыл бұрын
😍😍😍😍
@user-rz3id7nm6s4 жыл бұрын
genius
@peppybocan6 жыл бұрын
So the graph of a function is a piece of tangerine. Kinda like a cutout of an apple, ...
@timperry69486 жыл бұрын
I imagine a day when VR allows us to visualize this in three dimensions. Will we make huge advances in maths and sciences when we have entire generations who live in an abstract world?
@yerr2346 жыл бұрын
i'm pretty sure it is already a thing now
@cycklist6 жыл бұрын
Zed!
@ianmoseley99106 жыл бұрын
Portsmouth FC Yes being British I find the US pronunciation of "z" as zee slightly distracting, but thats my problem
@PedroTechnologies3 жыл бұрын
Bruh chill 3:03
@blblbl27506 жыл бұрын
blackpenredpenbluepen
@LiNa-nw2zb6 жыл бұрын
I've done it. Now a bit of sarcasm incoming However easiest solution would be to switch axis so x becomes y and y becomes x XD
@wubbalubbadubdub33522 жыл бұрын
How would you explain this to a blind person? You shouldn't have to rely so heavily on visualization. Math is about rigor.
@blackpenredpen2 жыл бұрын
?
@saturn_Il2 жыл бұрын
whats the point in doing something you dont understand
@elias694202 жыл бұрын
How would you show a book or a paper to a blind person? How would you read it aloud to a deaf person? What is this form of rigor that is accessible to absolutely all people?
@atulit6 жыл бұрын
Graph of y=x^2 is wrong
@laxmipapney71826 жыл бұрын
what is wrong about it?
@blackpenredpen6 жыл бұрын
Laxmi Papney i guess not pretty enough?
@JensenPlaysMC5 жыл бұрын
That moment when you are watching a video on triple integrals but cannot graph y=x^2
@777loveforever3 жыл бұрын
I'm gonna marry him someday I sware 🥰 Thanks uwu
@mrsam41134 жыл бұрын
Your videos are way too long and I can't understand pig latin