1. 6.2a DISKS METHOD (SOLIDS OF REVOLUTION)
Rita Korsunsky

2. Separate the
area into
rectangles of
equal length
Let’s revolve region under f(x) from a to b about x- axis
Revolve each separately to form many disks
Total volume =sum of volumes of infinitely thin
individual disks

3. Disk Method a b d c

4. Example. The region bounded by the graph of y = x2 + 1, the x-axis, and the lines x = - 1 and x = 1 is revolved about the x axis. Find the volume of the resulting solid.
1. Graph the Region and identify the thickness (dx or dy)
3.) Integrate
2.) Express the radius for one disk in terms of x (if dx) or y (if dy)

5. Example. The region bounded by the y-axis and the graphs of y=x3, y=1, and y=8 is revolved about the y-axis. Find the volume of the resulting solid.
Volume of Resulting Solid: 58.4

6. Example: Sketch the region R bounded by the graphs of and
from 0 to , and find the volume of the solid generated if R is revolved about the x- axis. 1 -1