https://youtu.be/NwdmGyQsqz0

In this video I go over another example on finding the volume of a solid or shape formed by rotating a region, and in this case, rotating the region about a vertical line. In this example I solve the region enclosed by the curves y = x and y = x<sup>2</sup> (same region as in examples 4 and 5) about the vertical line x = -1.

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# Integrals and Volumes: Example 6

![Integrals and Volumes Example 6.jpeg](https://cdn.steemitimages.com/DQmfYoDQ5sjKUQKb1No1jbTbqKoupkgpqzyP6LEkcEqVCkB/Integrals%20and%20Volumes%20Example%206.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 x = - 1.

**Solution:**

![](https://cdn.steemitimages.com/DQmXPCEaNLqKCD9VrhmgUGWzHcAYcZz6Qni1vJBtETBAfK5/image.png)

![](https://cdn.steemitimages.com/DQmSqkPTCAhKnutUXg5AUN8VF2SgMLUUTGeFdzQkimMnoYz/image.png)