The double integral sign is used to indicate mathematical integration performed twice in succession. Double integrals are used to calculate the integral s of function s in two variable s. An example is the volume under a surface in three-dimensional ( 3D ) space.
The double integral sign appears as two single integral signs, placed one after the other:
A typical expression for an indefinite integral of a function f of two variables x and y using the double integral sign is:
f ( x , y ) dx dy
In this expression, the function is first integrated with respect to x , and then with respect to y .