5.2. Volumes http://www.ck12.org
Volume By Cylindrical Shell about thex−Axis
Equivalently, if the volume is generated by revolving the same region about thex−axis, then the cylinders are
horizontal with
v=∫d
c^2 πrhdy,wherec=f−^1 (a)andd=f−^1 (b).The values ofrandhare determined in context, as you will see in Example 6.
Note: Example 7 shows what to do when the rotation is not about an axis.
Example 6:
A solid figure is created by rotating the regionR(Figure 15) around thex−axis.Ris bounded by the curvey=x^2
and the linesx=0 andx= 2 .Use the shell method to compute the volume of the solid.
Figure 15