Generalizations of The Reverse Double Integral

The general formula for a reverse double integral is:\[Integral]\[DifferentialD]x \[Integral]\[DifferentialD]y f(x,y)dx dy

Where f(x,y) is the function that needs to be integrated.The technique of performing a reverse double integral is to integrate the bounds of the inner integral with respect to the outer integrand,and to integrate the limits of the outer integral with respect to the inner integrand.This process can be summarized as:\[Integral]\[DifferentialD]y[\[Integral]\[DifferentialD]x f(x,y)dx] \[Integral]\[DifferentialD]x[\[Integral]\[DifferentialD]y f
(x,y)dy]
In other words,performing a double integral can be expressed mathematically as the following equation:\[Integral]\[DifferentialD]y[\[Integral]\[DifferentialD]x f(x,y)dx] \[Integral]\[DifferentialD]x[\[Integral]\[DifferentialD]y f(x,y)dy]=\[Integral]\[DifferentialD]x[\[Integral]\[DifferentialD]y f(x,y)dy]\[Integral]\[DifferentialD]y[\[Integral]\[DifferentialD]x f(x,y)dx]