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Cylinder Property

CYLINDER PROPERTY

Let m and M be the minimum and maximum values of f(x, y) on D and let A be the area of D. Then

12_multiple_integrals-39.gif

This corresponds to the Rectangle Property for single integrals. The solid with base D and constant height m is called the inscribed cylinder, and the solid with base D and height M is called the circumscribed cylinder. The inscribed cylinder and the circumscribed cylinder are shown in Figure 12.1.15. Intuitively, the volume of a cylinder is equal to the area of the base A times the height. Thus the Cylinder Property states that the volume of the solid is between the volumes of the inscribed and circumscribed cylinders.

12_multiple_integrals-40.gif

Figure 12.1.15 Cylinder Property

Here are two consequences of the Cylinder Property.

 
Home Multiple Integrals Double Integrals Infinite Double Riemann Sum Cylinder Property

Last Update: 2006-11-05