Volumes by Slicing (Calculus)

This calculus tutorial video explains finding volumes by slicing, also known as volume by cross section. We use illustrations and animations to show you how to use integration to find volumes by slicing, building the volume by integratiing the formula for the area of each cross section. We work examples that have the same base with square, triangle, and semicircle cross sections. An application of integrals that occurs commonly inn a Calculus 2 course.
0:00 Introduction
2:07 Example 1 (Semicircle cross sections)
6:42 Example 2 (Square cross sections)
8:42 Example 3 (Equilateral triangle cross sections)
Houston Math Prep Calculus 2 Playlist: • Calculus 2
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[@BattleWolf334]

you have no idea how many hours this took me to get and you explained it to me in 6 minutes (2x playback)

[@HoustonMathPrep]

2x speed for the win!

[@joshblank4579]

Thank you. This really helped me understand this a lot better.

[@HoustonMathPrep]

Awesome! Very glad it helped the topic make some sense for you :)

[@Safwan.Hossain]

The 60fps so smooth it's distracting me from the math content itself 🤣. Anyway, great video

[@HoustonMathPrep]

Thanks for noticing! LOL Glad you liked it okay.

[@michellegarcia9956]

thanks, I'm probably going to binge the rest of your videos now

[@HoustonMathPrep]

You're welcome, Michelle. Hope we are able to help you with some other stuff as well!

[@warrensalt999]

great video and amazing explanations! thank you very much.

[@newbloogeus]

great simple way of explaining without the confusion, thanks! My professor does a poor job of explaining in simple terms haha

[@HoustonMathPrep]

Thanks for the kind words of support, Kasey! Good luck!

[@munalisa4158]

Thank you sir. ❤️

[@jcarlos4458]

Thank you! You explained everything so easily! Helps a ton

[@HoustonMathPrep]

Glad it was helpful!

[@ishiitapal]

Thank you very much!

[@HoustonMathPrep]

You're welcome!

[@melisatuncer150]

Hi thank you for this video, I wonder what happens if I don't have any function to determine the area? I want to calculate the volume of a shape but I only know the height and radius of it.

[@compete247]

I guess I'm also curious about what happens if the bottom is not y=0 but another function?

[@HoustonMathPrep]

Hi Jessi,
If the bottom is not y=0, then this will affect the formula for the length of each "base" for a slice. Remember the length of the rectangles in this video are top minus bottom, which is √36-x² minus 0, or just √36-x². If you were to have a bottom function that is not y=0, then the length of your rectangle for the base would still be top minus bottom, or in other words: √36-x² minus (whatever you have instead of y=0). Good luck!

[@compete247]

@@HoustonMathPrep Wow! Thank you for clearing that up for me.

[@ItzZenga]

You know a video's good when there are 0 dislikes