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Homework Help: Method of Discs/Washers and Cylinderical Shells

  1. Jan 17, 2010 #1
    There's just something I need cleared up. When rotating around a line that isn't the x or y axis,I'm not quite sure what to do. Here are some problems:

    1) Find the volume of the solid that results when the region enclosed by y=√x, y=0, and x=9 is revolved around the line x=9.

    2) Find the volume of the solid that results when the region enclosed by x=y² and x=y is revolved about the line y=-1

    3) Use cylindrical shells to find the volume of the solid that is generated when the region that is enclosed by y=1/x^3 , x=1, x=2, y=0 is revolved about the line x=-1

    I know that with the cylindrical shells the alteration is within the X part of the formula (2π∫x*f(x)dx) but I'm not exactly sure how to alternate the other two. For example, if the function is √x will the thing become √(x+1)^2 or [(√x)+1]^2? If you could just show me how to do each problem, that would solve my problems :) I know you guys aren't supposed to show how to do the problem, but the only way you can answer my questions is with showing mehow to do it :)

    Thank you.
  2. jcsd
  3. Jan 17, 2010 #2


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    Start by drawing a picture.
  4. Jan 17, 2010 #3


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    Hi trogdor5! :smile:

    (try using the X2 tag just above the Reply box :wink:)
    If you're changing x, then you're replacing x by x - a, so y = √x becomes y = √(x - a).

    If you're changing y, then you're replacing y by y - a, so y = √x becomes y - a = √x.
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