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! :)

[@TheCommander454]

you made it so simple THANKS

[@kristakingmath]

Dhedan Saud You're welcome!

[@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! :)

[@bireshwarchakraborty7612]

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

[@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!!

[@SharvadharshiKBCE]

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

[@danterobinson2562]

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

[@moinaction]

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

[@Saqib7337]

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

[@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

[@Roman_CK]

Very clear and comprehensive. Glad I found your channel.

[@kristakingmath]

Thank you so much! ☺️

[@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

[@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

[@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. :)

[@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.

[@legslove3090]

This girl is a great teacher!

[@susannacook2870]

I love the way you teach this. Thanks!

[@kristakingmath]

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

[@zerodawn_rl8673]

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

[@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!

[@hassaanahmed23]

Thank u Krista YOU a REAL KING!

[@Petrolways]

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

[@Petrolways]

@@kristakingmath It went great , thank you

[@tasnimnahiyanpervez3071]

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

[@rbchaser1]

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

[@kristakingmath]

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

[@Sabiqyu]

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

[@kristakingmath]

+Sabiq Mufarrid Awesome! Thanks for letting me know.

[@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

[@KLCII88]

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

[@kristakingmath]

Thanks!

[@ishanrajpal5975]

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

[@kristakingmath]

So glad I could help, Tech! :D

[@maahi3534]

I couldn't understand this topic from book as it felt like writer has written in the script of Indus valley civilization. But ypu made it very simple. Thanks a lot.

[@kristakingmath]

You're welcome, Maahi! I'm so glad it finally made sense! :D

[@sukanyashukla3917]

loved the way you explained. Thank you! :)

[@kristakingmath]

Thanks! I really appreciate it. :)

[@gilmaferrer202]

Thank you! you make so easy and clear.

[@kristakingmath]

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

[@CASL-xq5zh]

crisp and precise... great video!

[@kristakingmath]

thank you very much!

[@8Trails50]

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

[@kristakingmath]

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

[@benripka6977]

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

[@kristakingmath]

Thanks, Ben! :)

[@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!! 🥰

[@0016mohit]

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

[@kristakingmath]

I'm glad I can help!

[@jiarong293]

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

[@kristakingmath]

Thanks, Fufu!

[@lasithaamarasinghe9251]

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

[@partharora16]

You make maths seems so simple ,thanks a lot

[@kristakingmath]

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

[@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 :)

[@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!!

[@alexandraprodanov4089]

you just saved me, thank you so much

[@swarnesh1093]

These videos are simply awesome.

[@kristakingmath]

+Swarnesh Jha yay! glad you like them!

[@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

[@padhaiwallah1900]

Thank you... It helped me alot

[@kristakingmath]

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

[@ANHNGUYENTHIKIEU-ez1ir]

So helpful

[@dob31121993]

Excellent explanation!

[@kristakingmath]

Thanks!

[@kennykwok1000]

Thank you for saving my calculus course!

[@peternganga7158]

Thanks

[@laithzyod8330]

YOU ARE AMAZING! Thank you.

[@swastikapokharel7385]

Thanks a lot ! I can understand now. ☺️

[@kristakingmath]

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

[@johnv4487]

Thank you for these videos! So helpful

[@sagnik489]

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

[@kristakingmath]

Thank you so much for subscribing! :D

[@rend_neu]

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! :)

[@rend_neu]

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

[@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

[@roberttaiswa9245]

thank you for the great tutorial.

[@oussamasouadka1156]

You are the best :)

[@MB-sx4bv]

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

[@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!

[@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).

[@financewithsom485]

You have told the trick behind every problem like this

[@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 !!!

[@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!

[@cupastasio]

perfect video

[@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. :)

[@gaurimandot5788]

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

[@kennethdavidsanchezgarcia2879]

Thank you so much, really ❤

[@soumyadeepization]

Very helpful...thank you very much

[@kristakingmath]

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

[@carlav5285]

Thanks for the great video!

[@kristakingmath]

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

[@qualquan]

This is really a double, not a triple integration problem. We first integrate Z.dy where Z is a function of (xy). Then convert the resultant integral function into a function of the height (x) and integrate a second time to obtain the volume. No need at all to integrate by dz which serves no useful function. This means our very first integration is Z=4-2x-y.dy to get an area integral. Then convert the (y) in the obtained area integral into (x) terms by substituting y=4-2x. This allows one to integrate the area integral which is now entirely in x terms over the height (x) to obtain volume. Alternatively Volume = 1/3 Area of base x height or 1/6 XYZ (1/6 2x4x4 =32/6 = 16/3)y area

[@BinuratheDarkLord]

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

[@kristakingmath]

Thanks!

[@tiisetsomashele1494]

you're amazing. thank you for the help

[@kristakingmath]

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

[@theatmosphere1229]

Thank you very much

[@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

[@mxame]

Really helpful. Thank you a lot

[@Kabaghe]

gotten something, thanks.

[@nehthang8265]

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

[@JamilKhan-hk1wl]

You showed the exact thing that i wanted to know

[@kristakingmath]

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

[@boonyewlee]

very well explaination

[@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?

[@tgates99]

THANK YOU!

[@kristakingmath]

You're welcome, Tyler! :)

[@1sunilento]

Great video. Thanks a lot!!

[@kristakingmath]

Thank you so much, and you're welcome!

[@sudheerkumar-hm7pr]

WoW...nice explanation.....

[@kristakingmath]

Thanks!

[@joshuamurray3841]

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

[@dianacruzr2687]

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

[@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 .

[@ashishranjan7175]

you saved my final sem exam. thanks a lot

[@kristakingmath]

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

[@normanreedus6673]

Thank youuuu

[@ahmedadel8658]

It so simple thanks ❤

[@kristakingmath]

You're welcome, Ahmed! 😊

[@katherine4386]

Thank you thank you thank you! 🙏🙏

[@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🤗🤗🤗🤗🤗🤗🤗

[@ahmedmghabat7982]

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

[@yaraismail1954]

perfecto

[@garvitkohli8598]

I love it thank you so much

[@kristakingmath]

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

[@Eng-Amer-Al-Najjar]

thanaan you thank you very very very much < you're a life saver !!!you are awesome thank you proffessor

[@PravyaTejaswi]

You are awesome!!.Thanks

[@nicholasgabaldon657]

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

[@AmeerHamza-bc4fh]

Good explanation...

[@kristakingmath]

Thanks!

[@edembansah312]

OMG!!!!!!!! You are so good! damn. Thank you very much

[@kristakingmath]

So glad it could help! :D