Calculus - How to find the bounds of a triple integral

This video shows how to find the bounds on a triple integral in rectangular coordinates using the method of collapsing. This method is also called the shadow method. Remember that you must describe the surfaces that you enter and exit in terms of the variable associated with the direction of movement.
▬▬ Chapters ▬▬▬▬▬▬▬▬▬▬▬
0:00 Start
0:05 What does a triple integral describe?
0:38 The method of collapsing
1:12 The bounding surfaces of the region
1:29 Example 1, dzdydx
2:49 Example 2, dydxdz
4:15 A note on keeping bounds simple
4:28 Wrap up information and ending
▬▬ Related Videos ▬▬▬▬▬▬▬▬▬▬▬
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[@Morpheus-zw4px]

searched for such a long time until i found someone like you who could explain it intuitively. also great visualisations and the keyword "collapse" helped a lot. thank you!!!

[@TheRealDanteeBravoo]

this man saves my life without knowing it

[@MySecretMathTutor]

Thanks! :^D

[@samayshah143]

the best lecture i've seen. this helped me tremendously

[@MySecretMathTutor]

Keep up the good work! :^D

[@avalong7686]

lifesaver. You explained collapsing clearly and the visual was very helpful.

[@jayven7306]

no bs, straight to the point awesome explanation, super useful love it!

[@elatior]

Thank you so much for making this video! The visuals were awesome and made it really easy to understand.

[@MySecretMathTutor]

Glad it was helpful! It was fun to make. :^D

[@francopaulnicolini]

So, before i saw this videos, i barely did manage to solve integrals in R3, but sir, you are actually incredible, you just explained how to analize the graphics of each function of the figure and that with the compression in it, after doing the Z axis, it's a lot more easy to understand, kudos to you

[@MySecretMathTutor]

Glad I could help! I wanted to do this video for a while, but had to search for the right program to really visualize it. :^D

[@adam83101]

have my final next week, YOU ARE A LIFE SAVER!! thank you so much :)

[@BariScienceLab]

Unbelievable. Really helped me visualize, thank you.

[@llama-pr6dn]

Perfect video! Everything wasn't diluted and straight to the point. Visuals helped greatly as well.

[@jitendrathakran9613]

Intuitively brilliant, thanks without bounds, God bless you

[@EchoLocoCJ]

You've explained this so much better than anyone else ive seen. thank you so much i have an exam in a few days!!!

[@MySecretMathTutor]

I hope it went well! :^D

[@connormichalec]

very helpful, well explained

[@shivangoudapatil5246]

this video literally opened my eyes , that were closed by my teachers illogical equations

[@MySecretMathTutor]

Glad I could help out! :^D

[@Wooepeke]

First time i comment on KZbin, this is the best explanation I have ever seen! Well done.

[@MySecretMathTutor]

Glad it helped! :^D

[@shantakhadka3246]

Thanks sir for this video ❤

[@HazImal99]

Thank you very much for the video, it really helps me to identify the limits. Btw, do you also make a video for polar coordinate?

[@MySecretMathTutor]

I haven't done a polar coordinates video for double integrals, or spherical for triple. These are both great ideas! I'll write them down. :^D

[@wassenaat]

Thanks this is great for my calc 3 final monday

[@10xprospect65]

holy crap this explained things 10 times better than my professor. he's really a great professor but for some reason just couldn't explain this concept very well, thank you so much

[@MySecretMathTutor]

Glad I could help!

[@ahmadb.e.k4629]

perfect . thanks a lot

[@480pixels]

holy crap thank u for this video, i was having such a hard time visualizing the bounds for these questions. you saved me for this next quiz

[@MySecretMathTutor]

You're very welcome! :^D

[@NPCtje]

very helpful

[@gamespotlive3673]

This was amazing. You should be payed a million dollars bro.

[@smashinbedrock4903]

this video goes crazy not going to lie

[@MySecretMathTutor]

Thanks! Its was a fun video to make.

[@tncreations1267]

What does the 'R' stands for at 0:14?

[@peperodriguezalcaraz2609]

crazy shit thanks

[@k2___2]

thank you so much

[@MySecretMathTutor]

You're welcome!

[@SpookyThe2nd]

That's quite a jump in difficulty from the last video about means 😂

[@MySecretMathTutor]

I agree! I picked this because the topic really needed some good visuals to understand, and I wanted to experiment with how to make them. I think this will be a great gateway for even more difficult topics. :^D

[@Filename46_fnaf_edits]

My secret math tutor more like my secret math teacher

[@MySecretMathTutor]

Awwww Thanks! :^D

[@jordancottone6563]

you have literally stopped me from crying over not understanding this. thank you.

[@MySecretMathTutor]

That's great! (not the crying part) Hope it is starting to make more sense. :^D

[@chittibabu6533]

Hi sir please do new videos

[@ridjxbdnjs_2995]

z=y+1 z=x^2+1 y=1

[@einsteingonzalez4336]

0:04 "When a triple integral is applied to a function, it gives us a hypervolume." Amazing... 4D volume?! How can that be used to find the volume of polychorons?

[@MySecretMathTutor]

That would depend on describing the boundary of the polychron as a function. For a lower dimension (2-D) you can see that this is pretty simple for a square. This would be a constant function with the bounds taking up the length of the other side. For an equilateral triangle, now we have to describe the area using two functions, one for the first side, and another for the second side. (You could save a bit of time using symmetry as well)

[@J-J-DEAR]

Sir i am an indian so sir please slowly teach

[@TUF3557]

You can always slow down playback speed, a feature present in youtube itself

[@J-J-DEAR]

@@TUF3557 thanks bhai

[@YourOrdinaryNecromancer234]

There are captions, read them

[@ahmadb.e.k4629]

perfect . thanks a lot