The discussion revolves around the interpretation of integral notation, specifically the expression $$\int_{\mathbb{R}^n}f\, \mathrm{d}^n x$$. Participants are exploring what this notation signifies in terms of integration with respect to multiple variables.
Some participants have provided explanations regarding the notation, indicating that the integral involves multiple variables and that each dummy variable represents a different parameter. The conversation appears to be productive, with participants seeking and offering clarification.
There is an emphasis on understanding the notation in a simplified manner, with requests for explanations suitable for beginners. The context suggests that participants are navigating through foundational concepts in calculus related to multiple integrals.
It means ##\int_\mathbb{R}\int_\mathbb{R}\ldots\int_\mathbb{R}f \,dx_1\,dx_2\ldots\,dx_n##Leo Liu said:Homework Statement:: .
Relevant Equations:: .
I saw it somewhere but I did't know exactly what it meant. Could someone explain it to me like I am 5? Does it mean we integrate with respect to x twice?
$$\int_{\mathbb{R}^n}f\, \mathrm{d}^n x$$
Thanks. Just need some clarification -- do x-n s represent the same parameter or different variables?fresh_42 said:It means ##\int_\mathbb{R}\int_\mathbb{R}\ldots\int_\mathbb{R}f \,dx_1\,dx_2\ldots\,dx_n##
Different variables. The integral is over a region in ##\mathbb R^n##. Each ##dx_i## is a different dummy variable, much the same as ##\int \int f(x, y) dx dy##.Leo Liu said:Thanks. Just need some clarification -- do x-n s represent the same parameter or different variables?