Applications of Double Integral
The applications of double integral are mentioned below:
- Double integrals are used to calculate the area of regions bordered by curves or surfaces in the xy plane.
- Double integrals can be used to calculate the volume of solid objects or regions in three-dimensional space.
- Double integrals are used to calculate the mass and density distribution of objects with varying density.
- In probability theory, double integrals are used to determine probabilities for events in two-dimensional probability density functions.
- Double integrals are used to calculate electric field strength and electric flux over surfaces in electrostatics.
- Double integrals are used in fluid dynamics to determine fluid flow rates and fluxes over surfaces.
Double Integral
A double integral is a mathematical tool for computing the integral of a function of two variables across a two-dimensional region on the xy plane. It expands the concept of a single integral by integrating the functions of two variables over regions, surfaces, or areas in the plane. In case two variables are present, we need to substitute the value of one variable in terms of the other. This technique becomes very difficult when we deal with multiple variables to calculate the areas and volumes under the curves. A double integral is very useful in such cases. In this article, we will learn about double integrals in detail.