Triple Integrals in Cartesian Coordinates | Volume between Surfaces

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We can use triple integrals as another method to find the volume of a region. In this example we have a top surface and a bottom surface, two different parabaloids. We write a triple integral that computes the volume between these surfaces. This works much as it did with double or even single integrals. We choose one "nice" direction to integrate first, then the second, then the third. The hardest part is setting the limits of integration appropriately.

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This video was created by Dr. Trefor Bazett. I'm an Assistant Teaching Professor at the University of Victoria.

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Finally, I've found someone who explains in the most beautiful way :-) ...YAAYY!! SUCCESS:))

madhumithatk
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Like always the visual style helps a ton. You already have helped me a lot in understanding these things. So thank you.

Junker_
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Bro’s the CEO of Calculus. Got a perfect score on my last exam thanks to these videos!

AndyOrtiz
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for anyone wondering, the volume in question is 9/4 * pi

udoberk
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If you were my maths teacher🏆, I would never skip class😂😂😂😂

ogunsadebenjaminadeiyin
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the idea you are explaining is so clear. thanks man!

edwarddi
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I'm sure you can do quadruple, quintuple, n-tuple integration if needed. I'm sure in string theory, they use 11 integrations or other fancy functions that do the same thing.

StaticBlaster
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I could never figure out how to even set up triple integrals when I took calc 3! This is amazing!

erikawanner
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This is a criminally underviewed video

isaac
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This helped a lot! Thanks! I just found it a bit confusing why the dz integral goes from blue to red instead of red to blue when the red paraboloid is below blue, but it really helps visualize how to set it up.

Lexyvil
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The best explanation in the entire internet ! ❤

devjyotiroy
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Lol, a couple of hours ago, I pondered exactly about the question, what a triple integral actually means. Now this video pops up. Thanks, Dr. Bazett!

flippert
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Any possibility of videos on the big topics and theorems at the end of vector calculus? Line integrals, surface integrals, divergence and curl, Green's Theorem and so on? I'm thinking of using your videos as the basis for a flipped calculus course. Thanks, Trefor.

henryharmon
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Like your approach to visualize all your words on graph. Well done!

olehborys
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Can I use polar coordinates instead of x and y??


Edit: nvm i got using polar too.

dumdum
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Great to see triple integral of the cones of maxiumum intesity for input of the two interfering sources on the x-axcis

ANJA-mjto
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Nice video, the colours and the images are really outstanding :)

sergiolucas
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my master gave us subject to explain in class when I searched it on YouTube I didn't get it even i saw your videos ....thanks 🌹

AyaNi
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Sir, very helpful video... 🤗🤗Thanku so much... 🙏🙏😊

nishugill
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You are awesome... i learned how to imagine higher mathematics

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