Integrals and Volumes by Cylindrical Shells

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In this video I go over an introduction to solving the volume of a solid formed by rotating a region about a line using the method of Cylindrical Shells. This method is useful when dealing with functions that make the volume integral difficult to solve when using the earlier methods which I covered in my earlier videos.


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Integrals and Volumes by Cylindrical Shells

Integrals Cylinderical Shells.jpeg

Some volume problems are very difficult to handle with the methods in my earlier videos. For example consider obtaining volume of the shape formed by rotating the region below about the y-axis.

Method of Cylindrical Shells

Easy way to remember: V = circumference x height x thickness

Now consider the volume of the solid obtained by rotating the region below about the y-axis.

Now this seems reasonable but a formal proof of this will be shown in a later video once I cover the concept of integration by parts.

The best way to remember using the cylindrical shells formula is to flatten a shell as shown below.



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