How to change the order of a triple integral
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- Опубликовано: 21 авг 2024
- 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
For the rest of the answer, including animations, see ruclips.net/video/P9ZF3pZJyko/видео.html
blackpenredpen graph of y = x^2 is wrong
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.
Moral of the story, hire art majors to help draw 3 dimensional graphs because that's the hardest part of the solution.
😂 I swear bro
Me and my classmates in calculus admiring the professor’s hand drawn graphs...
@@divisix024 while my prof is just shitting and didnt even draw anything!
or build it in minecraft like one of my classmates once did
@@ScholarStream_25 haha
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.
Thanks!!
Same
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
I would pay any amount of extra tuition if I could get quality lessons like this from my professors.
If you I can help
I love the way that the integral signs are in different colors!
Thank goodness people like you exist
why do they make us do this
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
Upload more on triple integrals bro
Three times two times one that's six quick maths
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.
nullplan01 Wow, that was amazing. I'm really looking forward to learning this stuff!
Majoring in math is the most hardcore way to learn how to draw that I've ever seen
Amazing content! I feel much more confident for my exam. Thanks x
This was very helpful! Thank you.
Glad to hear!! : )
Great work, Bprp, you have a great video up again.
Thank you very very much. This type of tool is much more common than one thinks.
My man taught me math and then flexed a toblerone on me. I feel ashamed and greatful.
Thank u.
wow... love from india
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?
Usially it is very hard or impossible to integrate in anyway besides the correct order in those problems
Please more multiverible calx!
Great explanation! I could understand it despite haven't even finished my calc 1 course lol
Your explanation is jst of next level🤘 ,u make things easier to get inside the head.
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?
Toblerone
Thank u sir u changed my life
so helpful! and I love your smile!
Wow
You're so good at it. The way you explain is beautiful m
very helpful! Thank you
Great content man
Me who can't draw to visualise: imma just use inequalities!
Thank you!!!! This is just what I needed
0:43
I tried to be like Gotenks
blackpenredpen LOL
this should be called something like "Shuffling a pack of integrals"
1 pac , 2 pac, 3 pac, 4/ 4 pac, 3 pac, 2 pac, 1/ You're pac, he's pac, no pacs, none"
0:43 Ok! Ok!
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.
that was awesome!
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
LOL you make me laugh. Thanks man!
why?
The Toblerone at the end lol
Please do an example where you have to find the bounds first
thanks dude . it was helpful :)
This is application for find the volume
Only if f(x,y,z)=1. Otherwise a triple integral corresponds are finding a 4d "hypervolume".
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).
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
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. :-)
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.
Watching at 2x before one night of exams!
in fact its a very good art lesson
Thank you sm
Thank you!
讲的太好了！
thats crazy black pen
if only my math teacher could draw as well as you
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
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
0:42 Suddenly, ninjutsu.
THANK YOU
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
Thanks for you video. You really save me for my midterm. xiexie
Good luck drawing this on a test lol
Nice.
Make videos on surface and itegral
Legend
Wouldn't it be easier to evaluate in cylindrical coordinates?
helpful
thanks
Triple integral. Yay!
Tq sir
when is your next stream going to be?
😍😍😍😍
but the z stops at 1-y WHY does the z-integral goes to 1?????
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.
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 ?
I accidentaly worked out the problem for y going from x to 1 ;-;
Why wouldn’t the boundaries of y be from 0 to 1?
cuz it's in terms of dz
Do you teach calc 3 as well?
Bruh chill 3:03
So the graph of a function is a piece of tangerine. Kinda like a cutout of an apple, ...
Any, even microscopic critic can be read?
What about dxdzdy?
genius
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?
i'm pretty sure it is already a thing now
Zed!
Portsmouth FC Yes being British I find the US pronunciation of "z" as zee slightly distracting, but thats my problem
blackpenredpenbluepen
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
I'm gonna marry him someday I sware
🥰
Thanks uwu
How would you explain this to a blind person? You shouldn't have to rely so heavily on visualization. Math is about rigor.
?
whats the point in doing something you dont understand
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?
Graph of y=x^2 is wrong
what is wrong about it?
Laxmi Papney i guess not pretty enough?
That moment when you are watching a video on triple integrals but cannot graph y=x^2
Your videos are way too long and I can't understand pig latin
*there there*
blackpenredpenbluepen