The multiple integral is a type of definite integral extended to functions of more than one real variable, for example, ƒ(x, y) or ƒ(x, y, z). Integrals of a function of two variables over a region in ℝ2 are called double integrals.The multiple integral is a type of definite integral extended to functions of more than one real variable, for example, ƒ(x, y) or ƒ(x, y, z). Integrals of a function of two variables over a region in ℝ2 are called double integrals.