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:
- Choose Beginning Calculus from the initial menu and press
.
- Use the arrow keys to move to the menu item Volume by Slabs, press
and
.
- At the prompt F(x) =, enter the formula
x^3 - x + 1
- Enter the bounds at the prompts
- x_0 = -1
x_1 = 1
- At the prompt for the number of approximating slabs, 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.
- After the disks are drawn, if you press then you will see
the numerical approximation:
