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

In summary, the conversation is about someone seeking help with integrating the equation f=exp(m*x) dx, where x=[x1, x2] is a vector of variables. There is confusion over the notation e^{m*x} and whether it should be divided or multiplied by m in the integral. The person asking for help is unsure how to integrate over an array of variables and suggests that the question should be moved to a different forum.
  • #1
jetzt
2
0
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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  • #2


So you want to find
[tex]\int e^{m \vec x} \, \mathrm d\vec x[/tex]
right?

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

(If everything is properly defined, you'd expect something like [itex]m e^{m \vec x}[/itex] of course)
 
  • #3


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
 
  • #4


Yes, we understood that. CompuChip's question was "what does [itex]e^{m[x1, x2]}[/itex] 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 [itex]e^{m\vec{x}}[/itex] divided by m, not multiplied by m.)
 
  • #5


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

1. What is the purpose of integrating the equation f=exp(m*x) dx?

The purpose of integrating this equation is to find the area under the curve of the function f=exp(m*x) between the given bounds x1 and x2. This is useful in many scientific fields, such as physics and engineering, as it allows for the calculation of important quantities like work, displacement, and momentum.

2. What is the general process for integrating this type of equation?

The general process for integrating this type of equation is to first identify the variable of integration, in this case x. Next, use the appropriate integration rules and techniques, such as substitution or integration by parts, to solve for an antiderivative of the function f=exp(m*x). Finally, evaluate the antiderivative at the given bounds x1 and x2 and take the difference to find the area under the curve.

3. Can the bounds x1 and x2 be any values for this integration?

No, the bounds x1 and x2 must be real numbers and x1 must be less than x2. In some cases, the bounds may also be limited by the behavior of the function, such as when the function has asymptotes or discontinuities at certain values of x.

4. How does the value of m affect the integration of this equation?

The value of m affects the integration of this equation in two ways. First, it determines the shape of the curve, as m controls the rate of change of the exponential function. Second, it affects the difficulty of integration, as certain values of m may require more complex integration techniques.

5. Are there any practical applications of integrating this equation?

Yes, there are many practical applications of integrating this equation. For example, it can be used to calculate the work done by a varying force, the distance traveled by an object with a changing velocity, or the growth rate of a population with a varying growth rate. It is also commonly used in statistics to find the probabilities of continuous events.

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