Thread: Shell method Volume of a solid problem

Here's the problem:

Use the Shell Method to compute the volume of the solids obtained by rotating the region enclosed by the graphs of the functions , and about the y-axis.

I can solve problems when I am given one or two functions, an interval, and an axis to rotate about...but I am completely lost on how to solve this kind of problem. Any help would be great, thanks>

Hello, calnix!

Did you make a sketch?

Use the Shell Method to compute the volume of the solid obtained
by rotating the region bounded by: about the y-axis.

Code:

                  |
      *           *     |     *
             *    |    *|
       *  *       |     |:*  *
        *         |     |:::*
       * *        |     |::*:*
           *      |     |*  :
      *       *   |   * |   : *
    - - - - - - - * - - + - + - -
                  |    1½   2
                  |

Formula: .

The two parabolas intersect at


We have: .

Go for it!

Thanks a lot! I didn't know I'd use the given x-value and then find the other for the bounds. Appreciate it a lot! If you don't mind, I have another problem:

Use both the Shell and Disk Methods to calculate the volume of the solid obtained by rotating the region under the graph of for about:
the x-axis:____
the y_axis:____

I need to find what values of the axis the region is rotated around. Would I just use the 0 and 13/3 for the bounds?