October 13th, 2011, 07:21 PM  #1 
Senior Member Joined: Sep 2011 From: New York, NY Posts: 333 Thanks: 0  Volumes By Cylindrical Shells 
October 13th, 2011, 08:34 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,167 Thanks: 472 Math Focus: Calculus/ODEs  Re: Volumes By Cylindrical Shells
(a) Well, let's see: Equating, we find: Since b is given to be positive, there is no real value of b satisfying the given requirement. For all positive b, we have: (b) Computing the solids of revolution: Again, there is no positive real value for b that equates the two solids of revolution. For all positive values of b we have: (c) Computing the solids of revolution: For all values of b, we have: I used the disk/washer methods for the solids of revolution, I recommend you using the shell method for parts (b) and (c) and see if our results agree. For part (a), I recommend integrating along the yaxis for an alternate method. 
October 14th, 2011, 06:17 AM  #3 
Member Joined: Oct 2011 Posts: 45 Thanks: 0  Re: Volumes By Cylindrical Shells
can it be done by changing the number sequence

October 14th, 2011, 03:56 PM  #4 
Senior Member Joined: Sep 2011 From: New York, NY Posts: 333 Thanks: 0  Re: Volumes By Cylindrical Shells
Lets see what I can do: a) Integrating with respect to I think the new bounds for would be from zero to , and I think this would give me the value of the area shaded in the graph below, by the integration: is not as straight forward because the two function do not intersect, so I'm not sure how to get the upper bound. I originally thought that if for some value 'b' they had the same I could use that value as I drew in the graph below, but now I see that that's not possible because that would mean they are both the same function. I should be able to set up the integral with what I know from the question from the question even if I don't have the bounds. I know and If I solve and for is but I dont think I can say > : At any rate if I put that together I would have which will obviously not work. Im a mess on this one, Im going to have to think about it. 
October 15th, 2011, 06:48 AM  #5 
Member Joined: Oct 2011 Posts: 45 Thanks: 0  Re: Volumes By Cylindrical Shells
the changing of the number sequence may be the key

October 15th, 2011, 09:17 AM  #6 
Senior Member Joined: Sep 2011 From: New York, NY Posts: 333 Thanks: 0  Re: Volumes By Cylindrical Shells
I don't know what you mean.

October 16th, 2011, 12:49 PM  #7 
Member Joined: Oct 2011 Posts: 45 Thanks: 0  Re: Volumes By Cylindrical Shells
number sequences get it the positioning of the numerals got it

October 16th, 2011, 12:53 PM  #8  
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,167 Thanks: 472 Math Focus: Calculus/ODEs  Re: Volumes By Cylindrical Shells Quote:
 
October 20th, 2011, 05:09 AM  #9  
Member Joined: Oct 2011 Posts: 45 Thanks: 0  Re: Volumes By Cylindrical Shells Quote:
 

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