Triple Integrals in Cartesian Coordinates | Volume between Surfaces

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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[@giovannianimbono17]

Pls Add subtitles for deaf people, it’s a little hard to catch all the words you’re pronouncing. Anyway great video!

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[@solaire7046]

It would have been easier to follow if the visual representation had its axis labeled.

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[@freakshow1010]

Sounds like New Rockstar Guy.

[@video_camera]

If x^2+y^2=3/2, why is the y limit going from -sqrt(3/2-x^2) to sqrt(3/2-x^2) but the x limit isn't going from -sqrt(3/2-y^2) to sqrt(3/2-y^2)? Why is the y gone?

[@marcuswassenius1862]

imagine putting so much work into the visuals but having the microphone of a nokia

[@AyaNi1214]

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

[@edwarddi3833]

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

[@Junker_1]

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

[@udoberk6647]

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

[@erikawanner7355]

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

[@olehborys1462]

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

[@Lexyvil]

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.

[@isaac5990]

This is a criminally underviewed video

[@dannyatherton7557]

Thanks a ton! Explained very well

[@AtliTobiasson]

Amazing stuff, thanks!

[@somiaelshemy9666]

that was very clear, Thank You!