How to change the order of a triple integral

How to change the order of the differentials of a triple integral?

For more calculus tutorials, please see @bprpcalculusbasics

[wkingston]

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

[duncanw]

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.

[SpencerRemy]

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

[ScholarStream_]

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

[marcioamaral]

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

[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

[fasebingterfe]

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

[msshedv]

Three times two times one that's six quick maths

[nullplan]

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.

[bernfernandes]

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

[mikemichalarias]

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

Thank u.

[gpmsmiy]

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

[MrCigarro]

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

[Prxwler]

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

[AkashdeepSingh-qqfw]

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?

[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?

[nvapisces]

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

[maymirror]

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

[sajidrizvi]

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

[eugltht]

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