Approximate, using cylindrical shells, the volume of the solid of revolution which is obtained by rotating the area of the region bounded by the graph of the function

the lines **y = 1**, **y = 3** and the **y**-axis around the
**x**-axis.

Using Microcalc:

- Choose
*Beginning Calculus*from the initial menu and press . - Use the arrow keys to move to the menu item
*Volume by Shells*, press and . - At the prompt
*F(y) =*, enter the formula1/y - Enter the bounds at the prompts
*y_0 =*1*y_1 =*3

- At the prompt for the number of approximating shells,
*N =*, enter 10 - and you will see the following graph of the approximating rectangles:
- Then you will see the rotation of each of these rectangles in turn. Press
to stop the rotation:
- Press any other key to continue the generation.
- If you press then you will see
the numerical approximation:
- If you press again, then you can better approximations by changing the value of N. 30 is the largest value of N which can be graphed.