Integrate the following equation f=exp(m*x) dx where x =[x1 , x2]

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Discussion Overview

The discussion revolves around the integration of the equation f=exp(m*x) dx, where x is defined as a vector [x1, x2]. Participants are exploring the implications of integrating a function involving complex variables and vector notation.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant seeks assistance in integrating the function f=exp(m*x) dx, specifically for a vector of variables.
  • Another participant questions the notation used, asking for clarification on what e^{m \vec x} represents and how it relates to the integration process.
  • A participant clarifies that x=[x1, x2] consists of complex variables and inquires whether the integration should involve one or two complex integrals due to the two variables.
  • Further clarification is requested regarding the definition of e to a vector power and its implications for the integral, suggesting that e^{m\vec{x}} should be treated as a vector.
  • One participant suggests that the question may be better suited for a different forum.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the notation and the proper approach to the integration, indicating that multiple competing views remain without a consensus on how to proceed.

Contextual Notes

There are unresolved questions about the definitions of the variables and the notation used, particularly concerning the treatment of e to a vector power and the nature of the integration over complex variables.

Who May Find This Useful

Readers interested in complex variable integration, vector calculus, or mathematical notation in physics may find this discussion relevant.

jetzt
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Dear

I am trying to integrate the following equation

f=exp(m*x) dx

where x =[x1 , x2] is a vector of variable could you help me please to find the solution when I would like to integrate like this kind of equations.

help appreciated

Best Regards
 
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So you want to find
\int e^{m \vec x} \, \mathrm d\vec x
right?

Can you first explain what that notation means?
Usually \mathrm d\vec x = dx_1 \, \mathrm dx_2 but what is e^{m \vec x} in this case?

(If everything is properly defined, you'd expect something like m e^{m \vec x} of course)
 


the x=[x1 x2] is array of variables where x1 and x2 are complex and m is
a constant. so my question how could I integrate the function over an array dx and should I have one or two complex integral ,I think so two may be because we have two variable in the array

thanks for the help
 


Yes, we understood that. CompuChip's question was "what does e^{m[x1, x2]} mean?" How are you defining e to a vector power? In order for the integral to make sense, e to a vector power, here, must be a vector. Can you give more context for the problem.

(And you would expect something like e^{m\vec{x}} divided by m, not multiplied by m.)
 


well i guess the question should be moved to the right forum
 

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