Expressing a triple iterated integral 6 ways (KristaKingMath)

► My Multiple Integrals course: www.kristaking...
Learn how to change the limits of integration and order of integration to express a triple iterated integral in 6 different ways.
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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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[@govou3000]

at 6:00 I think x^2 = 4 gives x = + or - 2 instead of sqrt of 2

[@qualquan]

correct

[@Default_089]

Thank you soo much test tomorrow and no clue how to even start these !! lol oh and bit confused @ 5:47 shouldn't x = +/- 2 not +/- (2)^(1/2) ? a

[@lauragibbs46]

I've never been told a methodical way of doing triple integrals like this. You've saved my life.

[@kristakingmath]

+Laura Gibbs I'm so glad it helped!

[@lazyDude77]

This is more efficient and reliable than the methods they teach us, not to mention easier to understand.

[@loganmacneil2092]

Your chart method is such an intuitive way of looking at things. Thank you Krista, this really helped!!

[@sagewaterdragon]

I only discovered your channel this weekend as I'm reviewing for my final - this is the most helpful, clear, incredible perspective on math that I've ever seen. Now I'm really considering subscribing to your website for my differential equations course next semester. I wish I had known about your work before I started college.

[@jakem3043]

Could you do a problem where the bounds of the original integral are given and then find the new integrals by graphing the bounds? I have trouble on how to slice the region.

[@pivotal-ai]

sqrt4 does not equal root2..

[@user-sx5kx3pq2i]

Brandon Jones yeah i was like what is she smoking

[@peterchow172]

dude yeah she made a mistake unfortunately

[@soubhaginimohapatra3587]

@@user-sx5kx3pq2i She was teaching in a so nice approach. She did it so correctly. Unfortunately if she made one mistake, u shouldn't comment like this. After searching so many videos i found it more clear and transparent.

[@sebastianrodriguez2111]

@@user-sx5kx3pq2i NSJSJJSJSJSJ

[@nawresalkhaffaf9257]

watching this 2 hours before my exam.....

[@kristakingmath]

I hope your exam went great!

[@ghubb]

watching 10 minutes before exam

[@emirmazlum8339]

@@ghubb watching during the exam

[@JoseRodriguez-tx1qz]

@@emirmazlum8339 Watching after exam :/

[@michellezhuang2483]

Hi Krista, the constant values for x should be 2 and negative 2 instead of positive and negative root 2.

[@muhammadomarkhayyamkhan3593]

I watched too many different videos and most of the people can not explain this order of integration very well. you made it so simple and help me too much. thank you very much.

[@kristakingmath]

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

[@thoranevans4832]

This is a godsend for those of us who suck at graphing and visualising. This is the only thing I've seen that actually makes sense at all.

[@kristakingmath]

I'm so glad it helped, Thoran! :D

[@brettruss3359]

dude your a living legend! this is like the 30th video ive watched from you on multi variable calculus!

[@jimenacastillo5726]

I just have to say thank you - thank you so much! Neither my textbook or online homework explained how to come up with the limits, which I think is the hardest step of evaluating the integral. This is genius!!!!!

[@johngonsalves5268]

Wow! The table is a stroke of genius. Thank you kindly for helping us make heads from tails or some kind of Cartesian equivalent :0)

[@kristakingmath]

+John Gonsalves You're welcome, I'm really glad it helped!!

[@ethanglenn8541]

This is a topic I have been struggling to Understand in Multivariate calculus for a long time now and you have made things very clear for me with this video!

[@kristakingmath]

+ethan glenn I'm so glad I could help!

[@charazor-el5636]

THANK YOU SO MUCH! My teacher didn't explain this well, and I was so grateful for this video, especially when you introduced the table! Thanks again, Krista!

[@kristakingmath]

You're welcome Emily! Glad it could help. :)

[@jacksonking8298]

Krista is the goat, saved me fr

[@jvrsshurricane]

That was the best possible explanation on how to do these. You're awesome.! Thank you very much Krista!

[@kristakingmath]

Aw thanks! Glad you liked it!

[@ozgurderince8727]

thanks for perfect explanation.I have taken this course 3 years . Now , I ' m clear

[@kristakingmath]

I'm glad it could help!

[@learnmathwithprivilege]

Our lecturers can’t explain like this 🥺.Thank you so much 🔥🔥🔥🔥

[@kristakingmath]

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

[@leozoo-z9m]

You are a lifesaver!

[@qualquan]

A soul less tour de force. Ought to explain at the outset thar 1) first we write an equation of one side expressed in terms of the other 2 sides. 2) we then integrate this equation (of the first side) over the next side to get an area and express them in terms of the 3rd side. 3)Finally we integrate this area over the 3rd side between definite limits to get a definite integral representing a numerical volume.

[@angeley0484]

What if you are given the limits of integration instead?

[@vegenzohrabian5340]

great lesson... is there a way to do it 9 ways with a solid bounded above z=x+y-2 and below z=0? I know how to do 6 from your lesson, is there 3 more ways... I was thinking of splitting the solid in 2 and triple iterate the integral with half the solid... I know I am looking at an isosceles triangle, if I am looking above the solid.

[@hhaushssh1373]

It cleared my doubt. Thanks a lot 🙏💕 from 🇮🇳

[@GermanSnipe14]

+/-2

[@kennethnondo3604]

should that be root of 2 or just 2??

[@nawareagan7720]

Thumbs up Ms. you've really helped me...thank you!

[@ovrissa5619]

I had to subscribe after watching. The limits of integration can be tricky but, you break it down..

[@katherine4386]

Please keep making videos like this to help everyone with calculus🙏🙏

[@kristakingmath]

😊

[@entertainmentbm7811]

Fantastic... I am to much worried about this topic. But after watching this video I am able to solve such kind of problem 😊😊🙂... Thank you ❤️

[@cinema187]

thank you, these originally just looked like a puzzle or something to me until I saw how to do them systemically

[@kristakingmath]

You're welcome, Cinemá! :D

[@devikabsree8087]

Though this video is very useful, this method can be applied only when its possible to form such a table. But look at this question : Find the volume under the surface x+2y+z=4 and above the circle (x^2)+(y^2)=4 in the xy plane. It's not possible to form the table in this case. Thank you as it has helped me to solve questions where I can form the table of limits.

[@jaydenma5311]

I have a similar question A solid in the first octant containing the origin and bounded by sections of the plane y = 1 + 2x and the sphere x^2 + y^2 + z^2 = 4 How can we expres in 6 ways? It seems that i cant use your method... Thank you.

[@lessthelonely]

Try intersecting both equations you have and then using the 3 equations you have! That third equation must be what you're missing!

[@blinkzyboi4921]

how do you use this method if you are only given the limits of integration

[@shitpostheavy]

BEST TIP EVER

[@danika1425]

Watching this the day before my test, thank you!! :)

[@kristakingmath]

You're welcome, Danika! I hope the test went great! :D

[@mathadventuress]

watching this 2 hours before my exam lmao

[@mariamhus4052]

this never made so much sense!!! calc 3 exam tomorrow! thank you

[@kristakingmath]

You're welcome, hope the exam went great!

[@ledzeppelin4892000]

Quick question: Does this work for any triple integral? I'm really bad at sketching and visualizing domains in 3 dimension. If so, this would be a godsend.

[@zehraxh]

I'm so glad I saw this

[@bapunapradhan6131]

Nice madam The steps are quite good. The steps you taught ....is very good.

[@kristakingmath]

Thanks a lot, Bapuna! 😊

[@nikhilsingh5863]

Spectacular explanation

[@kristakingmath]

Thank you so much, Nikhil! :)

[@levygwali1165]

how can we thank you enough for your great help?

[@Ensign_Cthulhu]

Thanks. I've always wondered what to do with these "general" problems in which no or few limits of integration are given. Do you have a vid that covers how to pick the best order, or is this something only gained by experience?

[@rajendramisir3530]

Terrific video plus the Jacobian one. Thanks.

[@kristakingmath]

Thanks, Rajendra! :)

[@Jeffrey_Wong]

your voice is so calming

[@MrJaros]

If I fall asleep to these videos with the playlist on loop, will I then be a math genius???

[@kristakingmath]

I'm not sure it works quite like that... but it's definitely worth a try! 😜

[@Zephyr-tg9hu]

Thank you, Krista!

[@kristakingmath]

You're welcome, Zephyr!

[@willalex7949]

This is so helpful. Thank you for making this video.

[@kristakingmath]

+Will Alex You're welcome, I'm so glad I could help!

[@liyuanyan5170]

Thank you so much!

[@jiajunyu2022]

Thank you for sharing this, it helps me a lot.

[@kristakingmath]

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

[@LauraLeyvaStaysafeStayinformed]

thank you so much! this is so clear and organized!

[@kristakingmath]

😊

[@HNunes-te2zm]

This is very very good. Thank you.

[@spencerjin8370]

My teacher didn't teach this.... thank you so much

[@kristakingmath]

You're welcome, Spencer! Glad it helped! :D

[@MA6manalac]

This is so good and still very valid. Thank you

[@abdo118sh9]

thank you so much what an easy way

[@kristakingmath]

You're welcome, Abdo, glad it helped!

[@jferro96]

this is genius. Will it work everytime? i didnt see it in my book, thats why im wondering

[@kristakingmath]

+J Ferro Yes, it'll work everytime!

[@J4MESRICH4RDS]

Does this always work?

[@sushantbhatta7759]

wow i just loved the way you explained without a graph. I just have a question; what if there was y^2 in the equation instead of y. You would get two values of y from the equations and have 0 as given values so what will be the limits. And also if y was equal to something else say 2 instead of 0 would we still be substituting the value of y as 0 in the equation or should we consider 2 instead? please reply . thank you

[@kristakingmath]

+Sushant Bhatta If you had y^2, then you probably wouldn't be given y=0, so you'd use those two original values.

[@sushantbhatta7759]

I have a similar problem and it does have a value of y. I am not very sure if u can really do these kindda problems without a real graph.

[@guycuul4979]

This helped me a lot! Thank you.

[@kristakingmath]

So glad it could help!

[@andrewhellman9939]

x^2 = 4, x = 2 not +/- sqrt(2)

[@franspigel9281]

Hi, I like your tutorials, they simplify the subject matter a lot, but sometimes perhaps too much. Like in this particular one, your method for finding the limits is flawed. By substituting 0 for different variables, say X and Y, you assume that Z achieves its limits on its own axis, which may or may not be true. If your condition was changed slightly, so it read y = 4 - (x-1)^2 - 4z^2, your method would produce +/-sqrt(3/4) as the constant limits of z, yet it still achieves +/-1 for x=1, y=0. I guess what I'm saying is, someone could assume that equating variables to 0 is a good method for finding limits, while it only works in some situations, and not in others.

[@ExperimentalWeapon]

Awesome explanation and great visuals!

[@kristakingmath]

Thanks, Jared! :D

[@Coconinga]

Thank you

[@ankitsadotra0]

Thats indeed the perfection .. love it.. thank u ..

[@greensasque]

What if the integral is not simple in x and y and you need to break it up into multiple domains?

[@saloksingh7]

Hi there. I have a similar question but the limits are defined by y^2 + z^2 = x and plane x=4. When finding the y(z) and z(y), we get y=√-z^2 and z=√-y^2 which is giving imaginary numbers. How would we proceed for such a problem?

[@jacksonking8298]

Did you ever get an answer for that?

[@thabangmthethwa7233]

this is awesome..its like a machine...

[@kristakingmath]

+Thabang Joel :D

[@asmarasim5968]

YOU ARE THE BEST!!

[@CarlosGutierrez-ln6tt]

What about if instead of the curves being our givens they already give us a triple integral and we have to change the order of integration, would this method work and how?

[@jacksonking8298]

did you ever get an answer?>>

[@christalmonasterio489]

Thank you so much!!! This has been really helpful.

[@kristakingmath]

You're welcome, Christal, I'm so glad it helped!!

[@phuongnguyen-kc8hi]

Thank you so much. It helped me a lot.

[@kristakingmath]

You're welcome, Phuong! :)

[@haidar3369]

hi, u r really good at math. there's a subject called (volume integral) it's just like triple integral but with (divergant) or something can u explain it pls?

[@mkusasakala3861]

Damn!!! thus what i was looking for.Thanks !

[@kristakingmath]

You're welcome!

[@yhyn6318]

thanks so much

[@Lombriga98]

Good job, thank you for the video!

[@kristakingmath]

Thanks!

[@aadams3316]

My Prof. taught us this section, then told us to go home and watch your videos.

[@briangarciahernandez7394]

this was really helpful muchas gracias!

[@kristakingmath]

De nada, Brian, I'm so glad I could help! :D

[@rachelleramirez5192]

Do all integrals have the same volume?

[@BeaStScoPesHD]

This is so great, thanks a lot.

[@kristakingmath]

:D

[@abhishekd2658]

Becker Lethc

[@PtotheMtotheJ]

Very helpful, thank you.

[@kristakingmath]

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

[@josephhunter4186]

Thanks! Super helpful!

[@kristakingmath]

You're welcome, Joseph, so glad it helped! 😊

[@gracehu3031]

thank you very much! :D

[@toviawoukomieli2461]

This is awesome!

[@kristakingmath]

Aw thanks! I'm glad you liked it!

[@sukibe2067]

doesn't work with my functions.

[@rashenwanniarachchi8158]

Thank youuuuu

[@muhammadusama5902]

So much helpful thank you so much 😍

[@kristakingmath]

You're welcome, Balaj! :D

[@inaamullah7192]

pretty nice explained

[@yasinuslu1618]

perfect technic, Thank you

[@kristakingmath]

:D

[@lasithaamarasinghe9251]

great video

[@CHRISTICAUTION]

saves me during corona thanks

[@girlsgenelegends6963]

OMG THANK YOU SO MUCH

[@kristakingmath]

:D

[@AymaneAbaich]

Very very helpful

[@mathadventuress]

you can generalize all of these... like you can say, set x or y equal to 0, solve for z...

[@thelolsaadlol]

what if there is more than one equation ?

[@InarusLynx]

I'd like to know as well. Say y =x^2 and y + z = 16

[@RDWize]

You said ''finding the volume'', you mean the hyper volume right??

[@ravutlanagaraju2777]

At 6:20 sec it's not √2 just +/- 2

[@wssz112]

love love love ur voice!!!!