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Integrals and Volumes: Example 5 Rotating About a Horizontal Line by mes

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mathematics · @mes · (edited)
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Integrals and Volumes: Example 5 Rotating About a Horizontal Line
https://youtu.be/1ISe3IuHjWQ

In this video I go over another example on finding the volume of a solid formed by rotating a region. In this example that region is the region enclosed by the curves y = x and y = x<sup>2</sup> (same as example 4) but rotated about the horizontal line y = 2.

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Watch Video On:

- DTube: [https://d.tube/#!/v/mes/QmXTdcXkXpJuKe9iHDm3YtbzLFsfb8Hfyxd2aLhu8eSpWK](https://d.tube/#!/v/mes/QmXTdcXkXpJuKe9iHDm3YtbzLFsfb8Hfyxd2aLhu8eSpWK)
- BitChute: [https://www.bitchute.com/video/kXlNO6Mz7lzK/](https://www.bitchute.com/video/kXlNO6Mz7lzK/)
- YouTube: [https://youtu.be/1ISe3IuHjWQ](https://youtu.be/1ISe3IuHjWQ)

Download Video Notes: http://1drv.ms/1qJli5V

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# Integrals and Volumes: Example 5

![Integrals and Volumes Example 5.jpeg](https://cdn.steemitimages.com/DQmawzirGtmkD1gtoHnbc95EDHv8QCfK2DEGuNTMogUF1ZM/Integrals%20and%20Volumes%20Example%205.jpeg)

**Example:**

Find the volume of the solid obtained by rotating the region enclosed by the curves y = x and y = x<sup>2</sup> about the line y = 2.

**Solution:**

![](https://cdn.steemitimages.com/DQmR4tynBN68JFfYP8kXPYUopWKLDwaxTVNhabhUmR76trD/image.png)

![](https://cdn.steemitimages.com/DQmVEDLLs6BxGn6k5K2BDxDWzyQ5XrLw4ZtbZYMq8hPk9g9/image.png)
👍  , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , and 166 others
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created2020-01-30 07:19:54
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vote details (230)
@maciejficek ·
$0.04
I really appreciate Your work.

Can I ask You to + that post of SchamanGerbert?
https://steemit.com/chess/@schamangerbert/steem-chess-tournament-february-01-the-winner-is-eniolw-last-edition#@schamangerbert/q52ohm
He was organizing a chess tournaments but he is unhappy bcs people are not interested. Of course I encourage You to observe his profile, sometimes he also puts beautiful photos of nature or airplanes.
👍  
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vote details (1)
@mes · 
Sounds good and just upvoted. Glad to help spread awareness of his chess tourney!
👍  
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@steemitboard ·
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Congratulations @mes! You have completed the following achievement on the Steem blockchain and have been rewarded with new badge(s) :

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