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Integration of two variable function

Note: This concept idea hasn't been proven yet or maybe mathematically incorrect. Any contribution would be greatly appreciated. Basic Knowledge of Integration and Functions In mathematics, usually we take x as independent variable and y as dependent variable. In General, a function is written as y=ax2+bx+c If we differentiate the above function, we get: dydx=2ax+b i.e   dy=(2ax+b)dx Generally, a Integral function is written as: f(x)=(2ax+b)dx Note: There is a wrong perception that, Integration give area under function, but actually, Definite Integration give area under a given function f(x) and Indefinite Integration gives an entire family of functions with an infinite number of members. Therefore, it is understood that:  f(x)=dy=(2ax+b)dx So, After clearing the basic knowledge, we can see how to Integrate something like this: f(x,y)dx   (where both x and y are variable)    Integration of two variabl...