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