https://youtu.be/3n6xQqNzN74

In this video I go over an example on finding the volume by using the method of cylindrical shells. The example involves solving the volume of the solid formed by rotating the region bounded by the functions y = 2x<sup>2</sup> – x<sup>3</sup> and y = 0.

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# Integrals and Volumes by Cylindrical Shells: Example 1

![Integrals Cylinderical Shells Example 1.jpeg](https://cdn.steemitimages.com/DQmeySK8YT3N7FxzemKGg4R4BT15dhRLXFRGbvfgTsqZZdd/Integrals%20Cylinderical%20Shells%20Example%201.jpeg)	

**Example:**

Find the volume of the solid obtained by rotating about the y-axis the region bounded by y = 2x<sup>2</sup> – x<sup>3</sup> and y = 0.

**Solution:**

![](https://cdn.steemitimages.com/DQmZrshi2AAoaomteZFgQgWVQM6n73emcC4eSSh2hFHC1Xa/image.png)

![](https://cdn.steemitimages.com/DQmVkMeAzKjaC8hZWZZEYqvh8eUpBmCXLgpPQq5oLQcG8pg/image.png)

Using the Cylindrical Shells method is easier than the washer method in this example because we do not have to solve for the local maximum value or write x in terms of y. 

But in later examples I will show that using the washer method and other methods from my earlier videos is actually easier than the cylindrical shells method.