When to use Disk vs Shell vs Washer

In summary, the conversation discusses the different methods (Shell, Disk, and Washer) that can be used for integration and how to determine which method to use. The main factor in deciding is looking at the cross sections of the area and determining if they are disks, shells, or washers. Experience and practice can also help in determining the easiest method to use. Sometimes one method may require splitting the integral into multiple parts, while another may not. In the end, a visual representation of the problem is the most important aspect in choosing the appropriate method.
  • #1
duki
264
0
Can someone explain to me when you should user the Shell / Disk / Washer methods? I don't understand how to determine which method to use.
 
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  • #2
Sketch a picture of the problem. Pick an axis to integrate along that looks like it will be the easiest. Now look at the cross sections of the area along that axis. Are they disks, shells or washers? You can do it more than one way. The picture is the most important part.
 
  • #3
I often sketch the picture and can't decide which method to use. Is there a way to tell which will be easiest for the given sketch?
 
  • #4
About the only difference is sometimes one method will require you to split the integral into multiple parts and another won't. There's no method I can describe in words, looking at the picture and experience will tell you.
 
  • #5
You know how sometimes you think about stuff for like three hours and can't figure it out... but then all of a sudden something just "clicks"?

That just happened... Thanks for your help!
I'm going to wait to mark this as solved to make sure I got it down.
 

1. When should I use the disk method?

The disk method should be used when rotating a two-dimensional shape around the x-axis or y-axis to find the volume of a three-dimensional solid. This method is commonly used when the cross-section of the shape is a circle.

2. When should I use the shell method?

The shell method should be used when rotating a two-dimensional shape around the y-axis to find the volume of a three-dimensional solid. This method is commonly used when the cross-section of the shape is a rectangle or a triangle.

3. When should I use the washer method?

The washer method should be used when rotating a two-dimensional shape around a horizontal or vertical line other than the x-axis or y-axis to find the volume of a three-dimensional solid. This method is commonly used when the cross-section of the shape is a ring or a donut shape.

4. Can I use any method to find the volume?

Yes, you can use any of the three methods (disk, shell, or washer) to find the volume of a three-dimensional solid. However, the choice of method will depend on the shape of the cross-section and the axis of rotation.

5. Are there any other factors to consider when choosing a method?

Yes, you should also consider which method will result in simpler integration and calculations. In some cases, one method may be more complex and time-consuming compared to another, so it is important to choose the most efficient method for your specific problem.

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