Problem:
Using the disk (slab) method, approximate the volume of the solid of revolution which is obtained by rotating the area of the region bounded by the graphs of the function

f(x) = x3 - x + 1

the lines x = -1, x = 1 and the x-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 Slabs, press and .
  3. At the prompt F(x) =, enter the formula
    x^3 - x + 1
  4. Enter the bounds at the prompts
    x_0 = -1 x_1 = 1
  5. At the prompt for the number of approximating slabs, 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. After the disks are drawn, if you press then you will see the numerical approximation: