How to change the order of a triple integral

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

[@blackpenredpen]

For the rest of the answer, including animations, see kzbin.info/www/bejne/hmq9d2amj6-sodE

[@atulit]

blackpenredpen graph of y = x^2 is wrong

[@yaleng4597]

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.

[@wkingston1248]

Moral of the story, hire art majors to help draw 3 dimensional graphs because that's the hardest part of the solution.

[@ScholarStream_25]

😂 I swear bro

[@divisix024]

Me and my classmates in calculus admiring the professor’s hand drawn graphs...

[@felikavalencia1933]

@@divisix024 while my prof is just shitting and didnt even draw anything!

[@D00000T]

or build it in minecraft like one of my classmates once did

[@bahuliyamanyapu7664]

@@ScholarStream_25 haha

[@duncanw9901]

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.

[@blackpenredpen]

Thanks!!

[@user-vm6qx2tu3j]

Same

[@SpencerRemy]

I would pay any amount of extra tuition if I could get quality lessons like this from my professors.

[@subodh373]

If you I can help

[@ScholarStream_25]

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

[@GreeeenT]

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

[@hafizmasum9600]

Upload more on triple integrals bro

[@marcioamaral7511]

I love the way that the integral signs are in different colors!

[@bernfernandes4380]

Amazing content! I feel much more confident for my exam. Thanks x

[@stephanm.tjaden3887]

This was very helpful! Thank you.

[@blackpenredpen]

Glad to hear!! : )

[@p1eboi804]

Thank goodness people like you exist

[@marinamaged962]

why do they make us do this

[@fasebingterfe6354]

Majoring in math is the most hardcore way to learn how to draw that I've ever seen

[@mikemichalarias8013]

My man taught me math and then flexed a toblerone on me. I feel ashamed and greatful. Thank u.

[@user-ms9sh2ed5v]

Three times two times one that's six quick maths

[@MrCigarro50]

Thank you very very much. This type of tool is much more common than one thinks.

[@sajalgorai2570]

wow... love from india

[@user-gp6ms5mi2y]

Great work, Bprp, you have a great video up again.

[@Prxwler]

Great explanation! I could understand it despite haven't even finished my calc 1 course lol

[@malaygangwar5956]

Thank u sir u changed my life

[@rybaplcaki7267]

Please more multiverible calx!

[@DawgFL]

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?

[@kylejohnson8447]

Usially it is very hard or impossible to integrate in anyway besides the correct order in those problems

[@AkashdeepSingh-qq5fw]

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?

[@nullplan01]

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.

[@andresxj1]

nullplan01 Wow, that was amazing. I'm really looking forward to learning this stuff!

[@briandutch7403]

very helpful! Thank you

[@user-eu5gl3th2t]

Thank you!!!! This is just what I needed

[@user-eu5gl3th2t]

0:43

[@blackpenredpen]

I tried to be like Gotenks

[@user-eu5gl3th2t]

blackpenredpen LOL

[@jadaayebae]

so helpful! and I love your smile!

[@maymirror]

Your explanation is jst of next level🤘 ,u make things easier to get inside the head.

[@nvapisces7011]

Me who can't draw to visualise: imma just use inequalities!

[@retired5548]

this should be called something like "Shuffling a pack of integrals"

[@sajidrizvi4665]

Wow You're so good at it. The way you explain is beautiful m

[@pberuto]

Great content man

[@Saunderabovo]

0:43 Ok! Ok!

[@VaehVay01]

Thank you sm

[@TheLychie]

LOL you make me laugh. Thanks man!

[@blackpenredpen]

why?

[@danajabaji4974]

that was awesome!

[@johnnychen4052]

讲的太好了！

[@tysonmotivationalvideos8220]

1 pac , 2 pac, 3 pac, 4/ 4 pac, 3 pac, 2 pac, 1/ You're pac, he's pac, no pacs, none"

[@sethhoisington2494]

Toblerone

[@fawfuls]

Thank you!

[@peanutbuttersmooth4849]

in fact its a very good art lesson

[@imankhalili7629]

thanks dude . it was helpful :)

[@Kgadi04]

Please do an example where you have to find the bounds first

[@BlurredLinez]

The Toblerone at the end lol

[@davidbrisbane7206]

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.

[@Koisheep]

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

[@nvidyyaa8919]

Thanks for you video. You really save me for my midterm. xiexie

[@silverwarrior1194]

THANK YOU

[@commissargamer]

Watching at 2x before one night of exams!

[@zacksbees329]

if only my math teacher could draw as well as you

[@TuanTruong-dg7xq]

thats crazy black pen

[@HD-dw7zk]

thanks

[@abofahad61]

This is application for find the volume

[@richardaversa7128]

Only if f(x,y,z)=1. Otherwise a triple integral corresponds are finding a 4d "hypervolume".

[@sergiokorochinsky49]

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).

[@richardaversa7128]

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

[@sergiokorochinsky49]

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. :-)

[@kevincaotong]

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.

[@connormichalec]

helpful

[@mandeepubhi4744]

Nice.

[@Hussain-px3fc]

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

[@sanchitkumar7357]

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

[@snipergranola6359]

Make videos on surface and itegral

[@TNTErick]

0:42 Suddenly, ninjutsu.

[@alyssagoins7485]

Wouldn't it be easier to evaluate in cylindrical coordinates?

[@fillername4223]

Legend

[@J.P.Nery.N.]

Good luck drawing this on a test lol

[@SteamPunkLV]

when is your next stream going to be?

[@davynrodocker8935]

What about dxdzdy?

[@yaleng4597]

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

[@HaitaoWang268]

Triple integral. Yay!

[@ram_2016]

Tq sir

[@iliasvrynas9189]

but the z stops at 1-y WHY does the z-integral goes to 1?????

[@user-el2pe5sh5v]

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.

[@theSASarethebest]

Do you teach calc 3 as well?

[@xy7914]

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 ?

[@abhiishekmuralidhar2565]

Why wouldn’t the boundaries of y be from 0 to 1?

[@drumman22]

cuz it's in terms of dz

[@siphilipe]

Any, even microscopic critic can be read?

[@srpenguinbr]

I accidentaly worked out the problem for y going from x to 1 ;-;

[@user-vm6qx2tu3j]

😍😍😍😍

[@user-rz3id7nm6s]

genius

[@peppybocan]

So the graph of a function is a piece of tangerine. Kinda like a cutout of an apple, ...

[@timperry6948]

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?

[@yerr234]

i'm pretty sure it is already a thing now

[@cycklist]

Zed!

[@ianmoseley9910]

Portsmouth FC Yes being British I find the US pronunciation of "z" as zee slightly distracting, but thats my problem

[@PedroTechnologies]

Bruh chill 3:03

[@blblbl2750]

blackpenredpenbluepen

[@LiNa-nw2zb]

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

[@wubbalubbadubdub3352]

How would you explain this to a blind person? You shouldn't have to rely so heavily on visualization. Math is about rigor.

[@blackpenredpen]

?

[@saturn_Il]

whats the point in doing something you dont understand

[@elias69420]

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?

[@atulit]

Graph of y=x^2 is wrong

[@laxmipapney7182]

what is wrong about it?

[@blackpenredpen]

Laxmi Papney i guess not pretty enough?

[@JensenPlaysMC]

That moment when you are watching a video on triple integrals but cannot graph y=x^2

[@777loveforever]

I'm gonna marry him someday I sware 🥰 Thanks uwu

[@mrsam4113]

Your videos are way too long and I can't understand pig latin

[@blackpenredpen]

*there there*

[@ssdd9911]

blackpenredpenbluepen