Triple integrals to find volume of the solid (KristaKingMath)

[@MrJaros]

this feels like learning parabolas back in high school...so simple. And yet approximately 5 videos ago, I was about to give up. i really really really appreciate this. You and KZbin teachers like you have helped so many countless students. Seriously, you've impacted the entire next generation of STEM. Thank you

[@skankhunt-zh1mo]

its been 6 years, does it seem so simple now?

[@samueldominguez253]

I like that you explain the "why" of steps. Thank you ! :)

[@kristakingmath]

+Samuel Domínguez You're welcome! Glad it's helping! :)

[@bireshwarchakraborty7612]

A crystal clear explanation that clarified my vague concepts regarding triple integration.

[@TheCommander454]

you made it so simple THANKS

[@kristakingmath]

Dhedan Saud You're welcome!

[@SharvadharshiKBCE]

@Krista King, you are truly a savior! Keep doing more of these videos. Thanks!

[@ricric4722]

Why don't teachers explain things this clearly? These concepts are so simple, but most teachers insist on making them seem like rocket science. Thank you so much for this amazing, simple, clear explanation!! This is the only video I found that really lays out the reasoning simply and clearly. Thank you!!!

[@kristakingmath]

You're very welcome, Ric! I'm so glad the helped and that everything made sense! :)

[@danterobinson2562]

Many years later you're still helping struggling students, thank you so much

[@zulyzappala4342]

You are the best Calculus teacher! I can easily get it. Ready for my final. Thanks a lot!

[@kristakingmath]

+zuly zappala Thank you so much! Good luck on your final, I hope it goes great!!

[@moinaction]

How could anyone thumbed down to such a great explanation? My math teacher couldn't even break it down like this

[@alimuhtasham4045]

it's been 6 hours i've been trying to understand this thing and you have done it for me. Thanks for saving me

[@tenafrancesallyana.4622]

THIS IS SO GOOD. You explain how and why each variables are obtained, how the order is dictated, why the upper limits sometimes uses equations rather than simple constants, etc. Very well-explained vid! Easy sub

[@Saqib7337]

Great job! finally i have honored with this tutorial. as i have an exam on Monday. really Helpful. Thanks!

[@gravewalker_0125]

As always, thank you so much for making a very complicated topic seem so methodical and easy to understand. Truthfully you have taught me more in Multi variable calculus than my textbook and professors combined and for that I'm indebted to you. God Bless.

[@kristakingmath]

I'm so glad I've been able to help! Thanks for letting me know. :)

[@Roman_CK]

Very clear and comprehensive. Glad I found your channel.

[@kristakingmath]

Thank you so much! ☺️

[@CodSock]

Absolutely loved the way you explained this for me. What a great video thanks for helping me on another topic. Love your videos.

[@kristakingmath]

Thanks for the comment. I'm glad you're liking the videos. :D

[@HoshikawaHikari]

Thanks for the clear explanation! Just needed to know how to set up the integral as I couldn't figure it out from my lecturer's notes.

[@susannacook2870]

I love the way you teach this. Thanks!

[@kristakingmath]

You're welcome Susanna! I'm so glad you liked it! :)

[@hassaanahmed23]

Thank u Krista YOU a REAL KING!

[@TheBoredVP]

Krista, thank you very much for the videos. They really help! I am enrolled in an online Calculus III course. Having access to these videos in lieu of a professor is great. Keep up the great work!!

[@kristakingmath]

Thanks, I'm so glad you like the videos... I know online courses are really tough!

[@zerodawn_rl8673]

Omg, thank you so much for not just showing us how to do it, but why as well this was beyond helpful😁

[@tasnimnahiyanpervez3071]

best video of triple integrals...u made it so easy!!! thanx a bunch

[@معاذ_الجمَّال]

YOU ARE AMAZING , i have a quiz in engineering math 1 tonight and you made that hard part look very understandable and easy, thank you

[@kristakingmath]

I'm so glad the video helped, and I hope the quiz went great!! :D

[@معاذ_الجمَّال]

@@kristakingmath It went great , thank you

[@rbchaser1]

Great Explanation! Very easy to follow choosing the limits of integration

[@kristakingmath]

Thank you so much, Roger! So glad it helped! :)

[@askarmukhammadov513]

Love your videos! I have an exam in 40 minutes and this video gives me confidence!

[@kristakingmath]

I'm so glad it helped, and I hope you're exam went great! :D

[@Prakashkumar-pg2vl]

you have to more describe about how integral of z(x,y) cover the entire area of tetrahedron but the video is helpful in understandig Thanks alot

[@Sabiqyu]

thank you so much it really helps me with my calculus finals!

[@kristakingmath]

+Sabiq Mufarrid Awesome! Thanks for letting me know.

[@KLCII88]

Thank you for this excellent explanation!! I have appreciated your videos over the past few semesters! :D

[@kristakingmath]

Thanks!

[@CASL-xq5zh]

crisp and precise... great video!

[@kristakingmath]

thank you very much!

[@ishanrajpal5975]

That's the exact thing i just needed. Thanks for the efforts

[@kristakingmath]

So glad I could help, Tech! :D

[@swarnesh1093]

These videos are simply awesome.

[@kristakingmath]

+Swarnesh Jha yay! glad you like them!

[@partharora16]

You make maths seems so simple ,thanks a lot

[@kristakingmath]

You're welcome, Parth! I'm happy to help! :D

[@kennykwok1000]

Thank you for saving my calculus course!

[@jiarong293]

ur explaination is good, and ur voice is sweet, great teacher

[@kristakingmath]

Thanks, Fufu!

[@sukanyashukla3917]

loved the way you explained. Thank you! :)

[@kristakingmath]

Thanks! I really appreciate it. :)

[@the_crazy_arrow]

hi today you solved two of the gratest mysteries that has been bugging me 1 how to use triple integral when " co-ordinate planes are given" and also how to evaluate an integral when there are no values given after the integral sign thanks to you i think i have a shot at my first semester exam in my college thank you Kristia :)

[@nehthang8265]

Miss for example if that the surface enclosed for z=4-X^2-Y.....not 2X...will the process be still the same

[@bellyup-qh2ut]

That was such an awesome video! Thanks for explaining it step by step, it really helped me out. Great job!.

[@kristakingmath]

I'm so glad it helped!!

[@jrt6722]

Why do we integrate dzdydx with 1 ? Why don’t we integrate the given function 2x+y+z=4, I’ve seen some volume-finding examples they integrate z in term of x,y but with 2 integral. Thank you so much

[@putnaik9144]

Its the same thing. If you watch her double integral and triple integral explanation videos, you'll see why. Integrating the function f(x, y) over dydz (dA) is the same thing as integrating as integrating 1dzdydx. It just comes down to the limits of integration. When she integrated just z in this case, she ended up plugging in the limit of integration z = 4 - 2x -y which is the same thing as f(x,y).

[@benripka6977]

You said all the right words... I appreciate you!

[@kristakingmath]

Thanks, Ben! :)

[@kailadavis8877]

Good video ! I'm a bit confused though, in some questions we are given a triple integral to work with and in some questions we don't (like in this one) and just given a z equation. When we are not given a triple integral to work with, do we assume it is equal to 1 dx dy dz.

[@kristakingmath]

You could be given a triple integral already, or you could be given a function and might need to put that function inside a triple integral and integrate that. Or, if neither of those is the case, then yes, you'll need to use 1 dx dy dz. :)

[@kristincotton3592]

So how can you use this method to solve the following problem: Find the volume of the region bounded by the equations x=y^2, x+z=1, and the x-y plane?

[@mdaley6]

This beats my book, professor, the tutoring center... you name it. Thank you so much! :)

[@kristakingmath]

Awww thanks Michael! So glad it helped! :D

[@8Trails50]

Calc III Final soon, thank you for the great video!

[@kristakingmath]

You're welcome! Good luck on the final!!

[@gilmaferrer202]

Thank you! you make so easy and clear.

[@kristakingmath]

You're welcome, Gilma, I'm so glad it made sense!

[@0016mohit]

Thanks alot! The video really helped me :) You are a great teacher, an amazing one!!!

[@kristakingmath]

I'm glad I can help!

[@Neamhain97]

Thank you for these videos! So helpful

[@ahmedmghabat7982]

Why cant we say bounds of Y [0,4] as shown in XY coordinates ?

[@joshuamurray3841]

Can the bounds of integration differ? EX: z [0, 4], y[0, 4-z], x[0, 4-y/2-z/2]

[@v8monster186]

Thanks very much to you ... but I haven't understood whats the difference between triple integral and double one's !!! It's staggering for me to make it out !!!

[@laithzyod8330]

YOU ARE AMAZING! Thank you.

[@Kosma_polvo]

Nice and comprehensive video... It'll certainly helps me a lot in my final exams :)

[@kristakingmath]

I'm so glad it helped, and good luck on your final exams, I hope they go great! :)

[@Kosma_polvo]

Yep.. It was so useful and hence helped me in my exams a lot, it was pretty great :)

[@Riiisuu]

So could you do it as: Z [0, 4] Y [0, Z-4] X [0, 2-Y/2-Z/2]?

[@vegetaiv9275]

Thank you so much! Thanks to your courses in Udemy, I did well on my college math courses.

[@kristakingmath]

You're very welcome! I’m honored!! So so glad that you had success in your college courses, that’s awesome!! 🥰

[@lasithaamarasinghe9251]

Thanks madam. I understood how to apply limits in triple integrals. 😊😊

[@alexandraprodanov4089]

you just saved me, thank you so much

[@roberttaiswa9245]

thank you for the great tutorial.

[@sagnik489]

Thnk you a lot , I was stumbling for a long time. Subscribed.

[@kristakingmath]

Thank you so much for subscribing! :D

[@dob31121993]

Excellent explanation!

[@kristakingmath]

Thanks!

[@ANHNGUYENTHIKIEU-ez1ir]

So helpful

[@namarikmanofal9169]

This is so much help ! Thank you for making me surviving my final .❤️!

[@kristakingmath]

I'm so glad it helped, and I hope your final exam goes great!

[@jy-dj4wl]

dont know if this is a stupid question or not , but when will we not be integrating by 1? as most of my school's triple integral arent usually integrating by 1 .

[@swastikapokharel7385]

Thanks a lot ! I can understand now. ☺️

[@kristakingmath]

You're welcome, Swastika, I'm so glad it helped! :)

[@abodejh9671]

Krista I have questions about triple integrals is difficult please can you help me

[@nicholasgabaldon657]

Why is the f function equal to 1? Shouldn't it be equal to the plane?

[@davemandyam4236]

Generally speaking, how do I decide weather to evaluate a volume with double integrals or triple integrals?

[@kristakingmath]

Usually you use triple integrals when you can't bound the function with just two curves, and instead you have to use three. For example, if you think about finding the volume between just two planes, then you could do it with double integrals. But if you have to find the volume between two planes and also underneath a sphere, you'd need three integrals to do that because you're trying to bound with three functions.

[@peternganga7158]

Thanks

[@padhaiwallah1900]

Thank you... It helped me alot

[@kristakingmath]

You're welcome, Padhai! I'm so glad it helped! :D

[@RobSummers993]

If you had a university, I would totally be a student! lol :) Thanks for making the videos so simple and right to the point. It really helps things click!

[@kristakingmath]

+Robert Summers I'm so glad you're liking them!

[@BinuratheDarkLord]

That was a great explanation. Thanks a lot @kristaking :)

[@kristakingmath]

Thanks!

[@gaurimandot5788]

Wowwwww!!!!Really fabulous explanation Mam. Start taking Zoom classes.:]

[@MB-sx4bv]

I really wanna appreciate you for this amazing video ........

[@oussamasouadka1156]

You are the best :)

[@financewithsom485]

You have told the trick behind every problem like this

[@tiisetsomashele1494]

you're amazing. thank you for the help

[@kristakingmath]

+Tiisetso Mashele Thank you so much, I'm happy to help!

[@thilodreyer7592]

is any order of integration simpler than the other orders ?

[@kristakingmath]

No, not consistently. It would always depend on the function being integrated, and the bounds of integration.

[@kennethdavidsanchezgarcia2879]

Thank you so much, really ❤

[@mxame]

Really helpful. Thank you a lot

[@technologyios]

Nice , triple integrals are also use for mass , right?

[@kristakingmath]

Yes, absolutely, you can use them for mass when the integrand is a density function. 👍

[@boonyewlee]

very well explaination

[@soumyadeepization]

Very helpful...thank you very much

[@kristakingmath]

+Soumyadeep Chatterjee You're welcome, I'm so glad it helped!

[@ashishranjan7175]

you saved my final sem exam. thanks a lot

[@kristakingmath]

I'm so glad I was able to help, Ashish! :D

[@carlav5285]

Thanks for the great video!

[@kristakingmath]

My pleasure, Carla, I'm glad you liked it! :)

[@maialqattanma]

why didnt you solve for all of variables by plugging zero. Why did you only do it for x?

[@gayathrim6148]

When X is x^2 what happened mam

[@katherine4386]

Thank you thank you thank you! 🙏🙏

[@theatmosphere1229]

Thank you very much

[@1sunilento]

Great video. Thanks a lot!!

[@kristakingmath]

Thank you so much, and you're welcome!

[@cupastasio]

perfect video

[@JamilKhan-hk1wl]

You showed the exact thing that i wanted to know

[@kristakingmath]

Oh good! I'm so glad it helped! :D

[@salami19-v4t]

LIFE SAVER

[@angelanasis7013]

Thank you so much!😘

[@dianacruzr2687]

I love you ^^. Thank you so much!!

[@GavinCOC]

THANK YOU

[@nickuhroo]

crystal clear!

[@Renatic123]

Thank you so much! Now this seems so understandable! :D

[@kristakingmath]

+Renato Afonso I'm so glad it's making more sense!

[@RahibulAzizAnam2002]

Thank you soo muchhh🤗🤗🤗🤗🤗🤗🤗

[@ahmedadel8658]

It so simple thanks ❤

[@kristakingmath]

You're welcome, Ahmed! 😊

[@taenyftw]

very nice. the half part of your video is quite a handful though lol. but maybe I'm just tired looking at so many numbers

[@tgates99]

THANK YOU!

[@kristakingmath]

You're welcome, Tyler! :)

[@PravyaTejaswi]

You are awesome!!.Thanks