Application of property V of double integrals

 Objective: apply the fifth property of the double integrals

Example:

Solution

The fifth property of the integral states:

This inequality represents also:

In the given inequality m = 2 and M = 13. Let's substitute them and f(x,y) in the inequality above:

Let's calculate the integrals of the constants 2 and 13 as well as that of the function f(x,y). This leads to write the following inequality:

 

Let's calculate the integral of the left and that of the right and then substitute:

Practice