Use the method of cylindrical shells to find the volume of the solid rotated about the line given the conditions:

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- August 29th 2006, 04:00 PMFLTRmethod of cylindrical shells
Use the method of cylindrical shells to find the volume of the solid rotated about the line given the conditions:

- August 29th 2006, 04:10 PMThePerfectHacker
Look at the picture.

Let us keep things positive.

Now you are rotating about

Let us shift the coordinate axes to the right 1 unit.

That means replace for .

Thus, your new curve is,

And you are rotating this time about the y-axis becase we shifted the curve.

Thus by cylindrical shells,

Note the new limits of integration because we shifted the curve. - August 29th 2006, 05:04 PMFLTR
once again i thank you for your paitence. To finish the problem I have came up with the following, however I feel something is wrong.

- August 29th 2006, 06:01 PMThePerfectHacker
I made a mistake. When you shift the coordinate axes to the right instead of it is .

- August 29th 2006, 07:06 PMFLTR
ok, based on that I have revised my anwser to this. Thoughts?

- August 30th 2006, 04:22 AMgalactus
Don't get disks mixed up with shells.