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I have one question about integrals. I know the definition of an indefinite or definite integral but I am not sure I understand the notation. The indefinite integral of a function f:R->R (assuming that it exists) is noted like this [itex]\int f(x)dx[/itex] Is the notation f(x)dx a multiplication or just a way of showing the variable of the integration?If we have an expression like this [itex]\int f(x) g(x)dx[/itex] then is this equivalent to [itex]\int [f(x) g(x)]dx}[/itex] or can we interprete it also like this [itex]\int f(x)[g(x)dx][/itex]. I was once told that this notation is just a convension but it can be treated like a product in cases like this: if u=g(x) then du=g'(x)dx then the integral [itex]\int f(g(x))g'(x)dx[/itex] is equal to [itex]\int f(u)du[/itex]. But I would like to know if this is really a product between the function and the infinitesimal or just a symbol that represents the meaning of the integral. If it's multiplication then I guess we could write also [itex]\int [f(x)dx]g(x)[/itex] ? (I also guess that the same explanation applies to definite,double and generally all integrals)

That's all. Thanks

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# Integral infinitesimal meaning

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