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July 6th, 2012, 09:14 PM  #1 
Newbie Joined: Feb 2012 Posts: 9 Thanks: 0  Difference between Disk/Washer and Cylindrical Shells
Just a question I have about these two methods of finding volumes of revolution. So, the formula for Disk/Washer is: Pi*Integral(f(x)^2dx)) The formula for Cyllindrical Shells is: 2*Pi*Integral(x*f(x)dx)) Do these formulae give equivalent results for every function in every interval? So, suppose we want to find a volume of revolution of the function y = x from 3 to 2 about the xaxis. We have: V = Pi*Integral(x^2dx)from 2 to 3 = Pi/3 * 27  Pi/3 * 8 = 19.8968 u^3 While, if we use the Cyllindrical Shells method, we will get the doubled answer.. I am pretty confused about this, but maybe I am doing something wrong, so does anyone mind explaining? 
July 6th, 2012, 09:37 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 464 Math Focus: Calculus/ODEs  Re: Difference between Disk/Washer and Cylindrical Shells
You will always get the same result regardless of the method you choose to find the volume of a solid of revolution. Using you example, we find: Disk method: Shell method: 
July 6th, 2012, 10:03 PM  #3 
Newbie Joined: Feb 2012 Posts: 9 Thanks: 0  Re: Difference between Disk/Washer and Cylindrical Shells
Right, it's because the functions of x is used in cylindrical shells method when it is revolving about the yaxis, not the xaxis. When I want to use the cylindrical shells method to find the volume of revolution about the xaxis, I need to rearrange everything in terms of y and then integrate. Correct?

July 6th, 2012, 10:25 PM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 464 Math Focus: Calculus/ODEs  Re: Difference between Disk/Washer and Cylindrical Shells
Yes. Often one method is easier to compute than the other.

July 6th, 2012, 10:36 PM  #5 
Newbie Joined: Feb 2012 Posts: 9 Thanks: 0  Re: Difference between Disk/Washer and Cylindrical Shells
All right, thanks, that clears all the confusion.


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