Applications of double integrals: calculating the area of a rectangular region using double integral and the volume of a solid with a particular condition

 Objectives:

1) Calculate the volume of a rectangular region

2) Calculate the volume of a region bounded above by a function f(x,y) with f(x,y) ≥ 0.

Applications of double integrals

As we saw from the definition of double integrals, a double integral is a volume of a region R. In this post, we'll study the volume of a rectangular region and the volume of a region bounded by a function f(x,y) provided that f(x,y) ≥ 0.

Volume of a rectangular region

If the region is rectangular, we just calculate the double integral of the constant function f(x,y) = 1.

Definition

The area of the region R is given by:

Example

Solution

Volume of a region bounded above by a function  f(x,y) ≥ 0.

Example

Solution

Practice