Triple integrals (KristaKingMath)

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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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?!”

[schrodingerscat]

Stress levels of your studies throughout
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

[jiwonkim]

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!

[Siddeo]

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

[OliviaThompson-]

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

[danielspiteri]

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

[veeds]

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

[livvycandy]

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 :)

[NicoMarcucci]

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

[nitishroat]

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

[johnholme]

Simple no nonsense explanation! Thanks.

[alenajarro]

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

[TheCommander]

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

[Ali-huev]

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

[kathleenfindlay]

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

[hayley]

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

[everbtw]

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

[BhanuPratap-sjew]

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

[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?