Problem:
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

f(y) = 1/y

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

Visualization:
Using Microcalc:

  1. Choose Beginning Calculus from the initial menu and press .
  2. Use the arrow keys to move to the menu item Volume by Shells, press and .
  3. At the prompt F(y) =, enter the formula
    1/y
  4. Enter the bounds at the prompts
    y_0 = 1 y_1 = 3
  5. At the prompt for the number of approximating shells, N = , enter 10
  6. and you will see the following graph of the approximating rectangles:

  7. Then you will see the rotation of each of these rectangles in turn. Press to stop the rotation:

  8. Press any other key to continue the generation.

  9. If you press then you will see the numerical approximation:

  10. 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.