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posted by  HI guys on 7/24/2008 9:03:48 PM  |  status: Live  

Find the volume of the solid formed by rotating the region enclosed by

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Find the volume of the solid formed by rotating the region enclosed by
x=0, \ x=
about the y-axis.

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posted by jarodbarnum on 7/24/2008 9:32:00 PM  |  status: Live
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This one will be easier to integrate along the x direction, so upper function minus lower function leaves:  
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posted by Betel on 7/24/2008 9:48:24 PM  |  status: Live
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The graph looks something like this:

    

The shell method will be the easiest here.
Each shell will have length 2πx, height y, and width dx.

    

The volume of each shell is L x H x W = (2πx)(7+x5)(dx)














Hope that helps!
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posted by leettab on 7/24/2008 9:51:11 PM  |  status: Live
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we can use the method of cylindrical shells to find the volume

since we are revolving around the y-axis we will integrate with respect to x

the height of our representative rectangle will be


the radius of our cylinder will be some value of x between x = 0 and x = 1  


the method of cylindrical shells is


Our integral for the volume will be





integrating we get

  the answer
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posted by Achilles on 7/24/2008 10:06:54 PM  |  status: Live
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Response Details:
Around y-axis use cylindrical or disk method
I used cylindrical
 height=7+x5


 
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