What is Double Integral?
Double integration in mathematics uses integration with respect to two variables. We do not need to convert the complete equation into one variable for double integral. Instead, we can integrate the function with respect to two variables also. This is very helpful in the case of functions where we are provided with only one function and no relationship between the variables is defined. In such cases, we cannot substitute the value of one variable from the relation. Thus, we use double integral to integrate the function. Double integral is mainly used to calculate the area of 2D surfaces or curves in mathematics.
Double Integral Definition
Double integral is defined as the integral of a function over an area represented as R2.
A double integral is represented as follows:
[Tex]\int_R\int_R f(x,y) dx.dy [/Tex]
If the region R spans over an area of [a, b] and then the above equation can be written as:
[Tex]\bold{\int^a_b\int^c_d f(x,y)~dy~dx} [/Tex]
Here f(x, y) is a function of x and y, and the two integration signs represent the double integral over areas [a, b] and .
In the case of double integrals the inner integral is solved first and then we proceed to solve the outer integral. The calculation of the integral proceeds in the normal way by treating one variable at a time. In this case, the equation is integrated w.r.t x first, and then the equation is integrated w.r.t y.
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.