Triple integrals (KristaKingMath)

► My Multiple Integrals course: www.kristaking...
Learn how to evaluate a triple integral. Find the volume of the region E which lies under the plane and above the region bounded by three curves.
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If you could use some extra help with your math class, then check out Krista’s website // www.kristakingm...
● ● ● CONNECT WITH KRISTA ● ● ●
Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student-from basic middle school classes to advanced college calculus-figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: www.kristakingm...
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[@schrodingerscat3912]

Stress levels of your studies throughout calculus------------------
calculus 1 - playing patty-cakes with Barney the dinosaur
calculus 2 - getting locked in a kitchen with two hungry raptors
calculus 3 - stuck under a flipped jeep with angry T-rex during electrical storm

[@kristakingmath]

😂

[@schrodingerscat3912]

lol

[@MoAntphonyMo]

pretty dam accurate looool

[@number1RabidPlatypus]

calculus 4: all the above but now in n dimensions

[@wolfsburggti4476]

calc 4 is like getting raped by the t-rex

[@jiwonkim9001]

HOLY MOLY I was trying to figure out the order of integration for whole day and you literally saved my life! I can't express hown much thankful I am!

[@heyitsneel]

I'm so glad I came across your channel! You're way better than my lecturer at explaining and demonstrating these concepts. Thanks so much!

[@kristakingmath]

I'm so glad I can help! :)

[@Siddeo]

zero dislikes itself tells your videos are amazing..thanks..it helped me a lot in my maths tests..

[@iam_topg]

you just tell the idiots to go and dislike the video by your comment

[@danielspiteri4964]

Life saver. Interesting that you did not even need to sketch the z-plane, but you deduced the limits from the equations.

[@OliviaThompson-007]

Bravo Krista. I was totally struggling to understand the order of integration until I watched this video. THANK YOU THANK YOU!!!

[@veeds74123]

you are a goddess. I have an exam on this tomorrow and you saved me. thank you!!

[@kristakingmath]

Good luck tomorrow! :)

[@livvycandy7281]

I’m so glad I found this video! I’ve been struggling with setting up the limits and order of integration, and your explanation was so clear and concise that this topic finally made sense for me. Thank you for posting these wonderful tutorials! They are such a huge help :)

[@nitishroat]

Saved my day by helping in defining boundaries of x,y,z

[@alenajarro7240]

I’m getting ready for my final. I spent ALL day trying to figure out triple integrals. Thank your for this!

[@NicoMarcucci]

Thank you, the set up is the hardest part and you've really helped me get it :)

[@kristakingmath]

awesome!! i'm so glad the videos have been helpful!

[@Ali-hu5ev]

Thankss Krista !! Your videos are helping me than the others like : Pro Leonard , Khan Academy and Chemistry tutor .

[@duaimrahim1718]

hey just to confirm that minimum value of z would be zero or 1 as the min of x and y is 0 then if we substitute in z=1+x+y it would give 1 not zero. kindly rectify if this is not the case...........

[@jackanderson6966]

Muniba Gulzar the lower bound for the z is zero because z = 1 + x + y and z = 0 are two separate planes that describe the area being integrated. When integrating you don’t put the minimum or maximum values of one/two variables into that of another to find your bound. When I do multi variable calculus I always draw out a coordinate system for the variable equal to one other variable and from there deduce the last variable similar to what was done in the video.

[@ev4662]

Patrick JMT got me through calc 1 and 2, now you’re my only hope left to pass Calc 3 😭😭 thanks for these vids 🙏🏽

[@kristakingmath]

We got this! 😊

[@MrJaros]

I tried Khan Academy, I tried PatrickJMT. Only when I came to this video did I understand triple integrals. Thank you for keeping these videos free.

[@kristakingmath]

Glad it could help! :)

[@TheCommander454]

Thank you so much , i'm preparing to my final exam and ur videos are really good and helpful .

[@kristakingmath]

Dhedan Saud I'm so glad the videos are helping! Good luck on your final exam!

[@johnholme783]

Simple no nonsense explanation! Thanks.

[@kristakingmath]

You're welcome, john, I'm so glad you liked it! :D

[@kathleenfindlay7018]

I've been procrastinating learning this topic for weeks because of COVID stress. Thank you so much I am no longer behind😊

[@kristakingmath]

You got this, Kathleen! Hope you're hanging in there, this is a crazy time!

[@saswatapatra5919]

ur speed of teaching is just perfect !!!

[@BhanuPratap-sj3ew]

God! i was worried for these concepts for triple integrals but now thanx to u :)

[@kristakingmath]

i'm so glad it helped!!

[@hayley3286]

wow i was so confused in class but this video totally clicked with me. THANK YOU!!!!!!!!!

[@kristakingmath]

You're so welcome! :D

[@fernandojubany687]

Wouldn't the bottom value for first integral( dz) z be= 1?( z = 1+x+y, and x and y are = > 0)

[@samuelatienzo4627]

Put 0:00 to 0:03 in 2x speed...
Also, you have very neat writing - this was a great explanation :)

[@Ensign_Cthulhu]

Great vid.
Silly question: I have, here and there on the net, seen videos evaluating volume with both double integrals and triple integrals. What I haven't quite grasped firmly yet are the general circumstances for which each approach is most appropriate (or sometimes necessary). The *double* integral seems to be good for when the volume is enclosed by two (and only two) mathematically clearly defined curved surfaces (including the upper and lower halves of the same sphere) _each described by a single function_; the *triple* seems to be _required_ for when an arbitrary volume is the product of enclosure by three such defined surfaces (top and bottom "caps" and the walls of a prism of arbitrary cross-section), _all_ of which require at least one function to describe them.
I suppose in this case the bounds Sqrt(x), y=0 and x =1 extended into the z axis define the "walls"; hence three bounding surfaces and hence triple integral.
Does that sound about right?

[@kristakingmath]

Yes, exactly! You're absolutely thinking about it the right way.

[@flunknuts6260]

You’ve helped me for the second time thx so much

[@kristakingmath]

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

[@PhanteusZ]

Can we also have the x and y limits of integration as:
for x, [x=y^2 , x=1]
and for y, [0,1]
that would also work right?

[@qualquan]

The central idea behind all triple integrals, to find volume (not really explained here) is to
1) First write the function or equation for the side with the most variables, which happens to be Z here. The function or equation must be in terms of the remaining sides ie Y and X.
2) Next we integrate over the side with the next more variable which happens to be Y = sq.rt. X in this case. This gives us the ZY area function which must be expressed in terms of the remaining side X.
3) This leaves us with a ZY area function in X term easily integrated over the 3rd side or X as a DEFINITE integral to give the numerical volume.

[@talhamustafa927]

I love you-R way of explaining Krista ;)

[@kristakingmath]

Thanks! :D I hope it helps! :)

[@nta699]

Great video, nicely done, clear and concise!

[@kristakingmath]

Thank you so much, Nizam! :)

[@bishalpoudel481]

your tutorials are so awesome and very effective thanks very much.....

[@kristakingmath]

Glad you like them!

[@brunocruz7842]

How i can calculate for plane : x+y+z= 2 and z=1 ?

[@AK-od5go]

The drawing is a little small, but nonetheless it helped me to understand it at the first time!
Greetings from TUM!

[@Vision_Voyagers]

you are good. and your voice so nice. thank you very much for this

[@danischw9180]

Girl if you don't get paid to do this, you should! So helpful.

[@kristakingmath]

Thanks, Dani, I'm so glad it helped! :D

[@shanyuhimo6960]

Wow... Dat was amazingly good explanation

[@kristakingmath]

:D

[@h3nnn4n]

My own personal savior :)

[@sajinshah2115]

Simple as that. Thank you

[@1409musiclover]

for the limits for x, I had 1 and y^2 and for y, I had 1 and 0 but still got the same answer. Why is that so?

[@JensenPlaysMC]

lower bound for x should be y^2 and upper bound is 1, with 0 to 1 for y. this method works because instead of saying how the y value changes with x you're saying how the x value changes with y. and then summing up the slices as if they were hozirontal instead of vertical slices

[@shamsulhaqrahimi2739]

Thanks I learned a lot from your videos...

[@yiminzeng9097]

Your video is very helpful thank you so much:)

[@kristakingmath]

I'm glad I could help!

[@oyungunahlar3700]

That's thoroughly explained thank you

[@kristakingmath]

:D

[@ivanereiz1533]

i like your video..am trying to learn integrals and calculus on my own..could you point me in some direction where and how should I start?... thank you

[@kristakingmath]

+Ivan Ereiz I would start with my Calc I, II and III playlists, which will take you from the beginning and walk you through everything. You'll find all of them on my channel page!

[@ivanereiz1533]

CalculusExpert.com thank you a lot i will try... :)

[@strober1997]

thank you for this!

[@kristakingmath]

You're so welcome! I'm glad it could help. :)

[@rafiullahhaidari9912]

Thanks

[@kristakingmath]

you're welcome!! :D

[@sergioandres8041]

You are a good person ;)
Thanks a lot (Y)

[@kristakingmath]

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

[@machisanigel]

Thank you soo much

[@kristakingmath]

You're so welcome!

[@paulrhyne4]

Do you like Calculus better than Algebra? I do, even though Algebra is alright too.

[@kristakingmath]

I like them both, but calculus is more fun because it's harder! :)

[@indandaindanda3940]

Wow she is so amazing..

[@bytesNscrews]

very helpful, thank you =)

[@kristakingmath]

i'm glad it helped!

[@relaxingzone3265]

U R AWESOME !!

[@kristakingmath]

You too! :D

[@abhishekbansal8551]

@1:04 x=1 is not a function
Btw gr8 video

[@karenroman290]

Hi! I was wondering is there any other way to solve for the limits of integration for x,y,x\z without graphing it. Problems become complicated and get harder to graph. Any insight will help, thanks :)
+CalculusExpert.com

[@xlxx3694]

She speaks so fast :))

[@kavyapitchika2450]

it is so help full tanqq

[@kristakingmath]

Glad it could help!

[@greenlizardballs]

stay amazing, sis :)

[@schrodingerscat3912]

you have the weirdest SN i've ever read

[@zain4019]

AHHHHHHH TEST IN 27 MINUTES

[@zain4019]

Also thanks for your help :)

[@kristakingmath]

Hope it went well!

[@kanivakil198]

0:00 My goodness! I thought I had my playback speed at 2X.

[@lucianoinso]

thanks! Didn't expected to find an explanation by such a cute girl :)

[@julianarrieta3125]

you have a nice voice lol

[@shamsulhaqrahimi2739]

Thanks I learned a lot from your videos...

[@shamsulhaqrahimi2739]

Thanks I learned a lot from your videos...

[@kristakingmath]

+shamsulhaq shams Glad you like them!